(CNN) President Donald Trump's choose-your-own-adventure of medical studies and advice has this week forced his coronavirus team's medical experts into awkward and often untenable positions, leading to what some describe as a baffling conundrum of when and how to publicly correct potentially dangerous misinformation.

This week alone, doctors on Trump's task force have gently walked back his proposition that subjecting the body to sunlight could act as a treatment for the virus. They've been more forceful in rejecting the suggestion of ingesting disinfectant. Earlier, a member of his team cast doubt on the country's testing capacity . And multiple officials indicated the virus would likely return in the fall, even though Trump said it may not.

The medical experts are now regularly faced with the choice of either publicly contradicting the President or letting inaccurate and even dangerous information go uncorrected. The consequences of either seem unpalatable.

Members of the panel are often caught off-guard by Trump's comments, a source close to the coronavirus task force said, adding the President's remarks sometimes seem "surreal" to the experts sharing the podium at the daily news conferences. One official said task force members can never tell what precisely Trump will absorb from their briefings, often picking something small and fixating on it during the televised news conference afterward.

Some members of the task force have become aware that their reactions to Trump are being captured on camera, leading the experts and administration officials to either remind themselves to remain expressionless as the President is speaking or to stay away from the podium in order to avoid the camera.

Through it all, the health officials have been required to balance their professional and medical integrity with an imperative to not run afoul of the President, who is notoriously attuned to loyalty and often does not take well to being publicly undermined. Mindful that their recommendations on social distancing -- which Trump ultimately adopted and later extended -- have helped mitigate the crisis, health officials on Trump's team have endeavored to remain in good standing in order for their advice to be heard.

It's a conundrum underlings have faced throughout Trump's administration. Faced with choices or behavior that ran counter to their ethics or training, officials often chose to remain silent to maintain their private standing, hopeful their influence would lead to better outcomes eventually.

The result of that calculus has never been clear cut. But as the nation faces a public health crisis with more lives at stake than any recent national security or economic decision, the position of experts is becoming more and more consequential.

Sunlight and disinfectant

The episode involving sunlight and disinfectant illustrated the fraught position of Trump's doctors.

It was only two weeks ago that the White House got word, in response to its inquiries, that heat and humidity may not cause a decrease in coronavirus cases. After receiving a request from the White House Office of Science and Technology Policy, researchers at the National Academies of Sciences, Medicine and Engineering delivered a report on April 7 indicating a "decrease in cases with increases in humidity and temperature elsewhere should not be assumed."

That ran counter to what Trump had been suggesting for weeks : that warmer weather may cause the spread of the virus to slow. The report went unmentioned during the President's daily coronavirus briefings.

This week, when another government report emerged showing that sunlight might have an effect in killing the virus in the air, it was a different story. After seeing news coverage of a leaked version of the report, Trump called in the head of the Department of Homeland Security's science division that produced it for a private briefing in the Oval Office. He liked what he heard so much that he invited the official, William Bryan, to present the same information to the media during his early evening briefing.

But when Trump began raising unfounded speculation about using sunlight and disinfectant to kill the virus in human bodies -- which he claimed a day later was sarcasm -- things began going awry. A pained-looked Dr. Deborah Birx listened carefully as Trump mused about "cleaning" bodies with disinfectant. When Trump asked her about using "heat and light" as a treatment, she demurred.

"Not as a treatment," Birx, the White House coronavirus response coordinator and public health expert, replied. "I mean, certainly fever is a good thing. When you have a fever, it helps your body respond. But not as -- I've not seen heat or ... "

Trump cut her off -- "I think it's a great thing to look at" -- before moving on.

A Trump adviser working with the task force admitted to feeling an immediate visceral reaction to Trump's comments suggesting people could inject themselves with sunlight and disinfectants as a cure for the virus.

"I wanted to hide," the adviser said. "It was a tough moment to watch."

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Some of the experts on Trump's task force are concerned if they speak out too forcefully in opposition to what Trump is saying they could be removed from the effort to combat the virus, according to people familiar with the matter.

How each medical expert approaches the situation has differed. Dr. Anthony Fauci , the nation's top infectious disease expert, isn't hesitant to offer unvarnished thoughts or analysis even when it seems to contradict the President. This week, Fauci has offered a message on the potential return of the virus that ran counter to Trump's own, more optimistic projections -- including the President's suggestion that it's "possible it doesn't come back at all." Fauci's message was different: "There will be coronavirus in the fall," he said bluntly, adding later: "I am convinced of that."

The question of the return of the virus was prompted by an interview Dr. Robert Redfield, the director of the US Centers for Disease Control and Prevention, gave to The Washington Post . In it, he warned that the confluence of flu and coronavirus could make for a dire brew of illness.

Trump, apparently outraged at coverage of the interview, claimed Redfield had been misquoted. After declaring on Twitter earlier in the day that Redfield would be issuing a clarifying statement, both men appeared in the briefing room and Trump instructed Redfield to speak.

"I didn't say that this was going to be worse. I said that this was going to be more difficult," Redfield said. But pressed on whether the words printed in The Washington Post were what he said -- and not, as Trump said, misquotes -- Redfield affirmed they were.

A few days later, Trump was forced to confront another interview, this time one Fauci gave to Time Magazine . In it, Fauci said the US needs to "significantly ramp up" testing. "I am not overly confident right now at all, that we have what it takes to do that," Fauci said.

During Thursday's coronavirus task force news briefing -- which Fauci did not attend -- Trump addressed Fauci's remarks: "I don't agree with him on that, no, I think we're doing a great job on testing."

Blunt candor hasn't always endeared Fauci to Trump; the President has complained in private when it seems he's being contradicted by the nation's top infectious disease specialist.

Birx, who was detailed from the State Department to act as the White House coronavirus response coordinator, has chosen a somewhat different approach. Aides describe her as patient in meetings with the President, even when he is offering lengthy medical opinions or theories that have little basis in science. Instead of interjecting or cutting Trump off, she has waited for him to finish before laying out more reality-based ideas.

Some officials working with the task force have wondered whether Fauci and Birx -- who have known each other for decades and have what each describe as a mentor-mentee relationship -- are actively calibrating their tactics into a "good cop, bad cop" approach. Others who are familiar with the dynamic say each is merely operating as a public health professional and presidential adviser amid the highest-stakes crisis of either of their careers.

Whatever their thinking, their approach has seen some success. Using dire projections about potential deaths and alarming charts drawn up by a team of modelers, Fauci and Birx convinced Trump during an Oval Office meeting in late March to extend his social distancing guidelines for another month, even as the economy cratered. And this week, Birx privately convinced the President that it was too early for Georgia to lift restrictions on certain businesses, leading to Trump's rebuke of the state's Republican governor.

Camera time

After near omnipresence on television and in the daily press conferences during the earlier days of the outbreak, Fauci has taken a less prominent role in recent days. He appeared at Wednesday's briefing but was absent the previous four days. And while he gave an interview to ABC News earlier in the week, his media appearances have been lower-profile, including an appearance during Thursday's NFL draft

A source close to the coronavirus task force said Fauci is spending less time at the briefings and more time on vaccine development and other efforts aimed at combating the pandemic. After initially serving as a fixture at most briefings when the task force was first launched, Fauci now waits on White House officials to call him to the West Wing for the more Trump-focused news conferences.

Unlike Fauci, Trump sees Birx as a required presence at the briefings, sources say, given her colorful, detailed charts that reveal data about the outbreak throughout the US. Still, there have been questions about whether she is overly deferential to the President, even when his statements in public run counter to science.

She has drawn some criticism in recent days for refusing to publicly second-guess Republican governors who are opening their states well ahead of the federal recommendations. Comments she made in March about Trump's working style -- "he has been so attentive to the details and the data" -- were also lambasted as overly obsequious by some on the left.

Her slightly bewildered response to his question Thursday on using sunlight as a treatment for the virus suggested it was not a proposition he'd raised previously. And a source close to the task force said Trump had also not previously raised the idea of injecting disinfectant, including in the briefing from Bryan, the Department of Homeland Security official, earlier in the day.

On Friday, Trump claimed his comments were sarcastic and made "to see what would happened." But the suggestion nevertheless prompted loud outcry from medical experts and even from Lysol, the major maker of disinfectants

Asked about Trump's suggestion during a CNN Town Hall on Thursday evening, the head of Trump's Food and Drug Administration, Dr. Stephen Hahn, was also forced to offer this advice: "I certainly wouldn't recommend the internal ingestion of a disinfectant."

Even the White House itself tacitly offered its own health guidance in the form of a correction to the official transcript of Thursday's briefing. Sent on Friday morning, the new transcript corrected Birx's response to Trump's question about using sunlight as a treatment. Initially, the transcript quoted Birx saying "that is a treatment;" the accurate version read "not as a treatment."

It was not the first time medical experts -- including those on Trump's own team -- have cast doubt on his treatment theories. Fauci has cautioned in public and private that the treatment Trump has touted the loudest, the anti-malarial drug hydroxychloroquine, hasn't yet proved effective.

Trump has largely stopped raising hydroxychloroquine in public, and his favorite television network, Fox News, has also ceased its once-frequent coverage of the drug. Still, Trump denied he'd given up on the drug during Thursday's briefing.

"We've had a lot of very good results and we had some results that perhaps aren't so good," he insisted. "I don't know. I just read about one, but I also read many times good. So, I haven't at all."