If you’re shot, stabbed, hit by a car, fall off a roof or suffer any other major injury in San Francisco, you’ll be whisked to San Francisco General Hospital, the only trauma center in the city.

You’ll probably receive top-notch care at the renowned public hospital. But you may leave with a very unpleasant side effect: a shockingly high bill.

That’s because S.F. General — whose patients are overwhelmingly poor and are on Medicare or Medi-Cal, or have no insurance at all — lacks a good way to deal with patients who are actually insured. It exists mostly to serve as the city’s medical safety net, an admirable mission but one that neglects financial fairness for hundreds of patients with health insurance every year.

The trauma center has no contracts with private insurance companies. If it did, there would be agreements with those insurers on how much a particular drug or a particular procedure costs.

Instead, the hospital charges the highest rates approved by the Board of Supervisors and the mayor, receives whatever amount the patient’s insurance company decides to pay, and bills the patient for the rest.

And those bills are not small.

The supervisors and Mayor London Breed approved the current rates, which, according to the ordinance, are “proper reasonable amounts.” Those rates went up 6 percent in 2017 and another 6 percent in 2018, and are set to rise 7 percent July 1.

The current rates include $29,924 for setting foot in the hospital with a major trauma, $3,256 for the first hour in the recovery room, $2,605 for the second hour and $1,954 for each additional hour. (Sounds like the world’s most expensive parking garage.)

Not surprisingly, the bills patients receive can be stunning.

Leigh Honeywell knows the odd setup all too well. The Canadian had just moved to San Francisco in 2014 when she was walking in the rain to see a comedy show at the Punch Line, slipped on a wet pile of leaves and careened into a metal bike rack. She slammed her arm against the rack, felt a sharp pain and dizziness, and wondered if she’d broken a bone.

Her friends called a Lyft, and the driver said S.F. General was her best bet.

“I’m Canadian — you just go to the hospital, right?” she quipped, nodding to her country’s publicly funded, mostly free health care system. Her first visit to an American emergency room would be much more complicated.

“I get it X-rayed and looked at by a doctor for, like, 30 seconds,” recalled Honeywell, 34, the founder of a computer security company. “I didn’t have a broken arm.”

Good news, right? Well, not really. She received a bill a few weeks later for $3,004, which seemed awfully high for an X-ray and a few sentences from a doctor.

Honeywell paid a deductible of $300, her insurance company paid $1,257.27, and there was $1,446.73 left. The hospital insisted she pay it.

“For a couple minutes’ visit, it was totally unreasonable,” Honeywell said. “I’m trying to think of a time in Canada where I actually had to pay for something health care-related.”

She spent months and way too many phone calls trying to sort it out. Her extensive notes include dates and tidbits like “Called city, spoke with Janet” and “called and left vmail with SFGH.”

In May 2015 the hospital sent the bill to collections, and Honeywell hasn’t heard anything recently. Rachael Kagan, spokeswoman for the Department of Public Health, wasn’t able to say what happened in the case.

Here’s another one: A 26-year-old San Francisco software engineer said he visited the S.F. General emergency room in 2017 after an untreated cut on his finger became infected, swollen and painful. It was the closest emergency room to his office.

“Obviously, it’s a well-known hospital being the Zuckerberg hospital,” he said, withholding his name because he doesn’t want to remind the hospital he still owes lots of money. “I didn’t think too much about it.”

He said a nurse saw him for five minutes, drained the pus and gave him antibiotics. He received a bill for $5,082.60. His insurance company paid $2,890.74, and he was charged $2,191.86. After months of wrangling with the hospital and his insurance company, he’s not sure where things stand and is hoping the matter just goes away.

These stories could have been worse. A recent Vox article, which first shed light on this seemingly unfair billing system, told the story of Nina Dang, who broke her arm in a bicycle accident and was charged $24,074.50 by S.F. General. Her insurance company paid $3,830.70, and she was responsible for the rest. It also described the experience of Alicia Rodriquez, who went to the hospital with a migraine and owes more than $10,000.

In the Vox story, hospital spokesman Brent Andrew said, “We feel like we have to recoup what we’re able to from people who are insured because we’re supporting people who don’t have insurance.”

Charging those with private insurance eye-popping bills — bills their insurance is only partly covering — just so the hospital can cover those without insurance doesn’t seem fair, especially since S.F. General is part of a city government with an annual budget of more than $11 billion. Is $20,000 from a woman with a broken arm really going to make a difference?

Andrew didn’t return a request from The Chronicle for comment, but Kagan, spokeswoman for the Department of Public Health, of which the hospital is a part, said any insinuation that S.F. General is intentionally hitting up those with private insurance to help pay for poor patients is off the mark.

“That isn’t what’s going on,” Kagan said. “We know this is a problem for a small number of patients, and we are trying to work on solutions.”

Last year the hospital treated 108,000 people, and just 6 percent of them had private insurance. Kagan said there just aren’t enough patients with private insurance to make it worthwhile to enter into contracts with those insurers.

Under state law, the practice of “balance billing” — sending a bill to a patient if his or her insurance company doesn’t pay the full requested amount — is illegal for people insured through a health maintenance organization. Kaiser is an example of an HMO, a network of doctors that supplies services to its members.

But California doesn’t ban balance billing for those insured through a preferred provider organization, which pays more for services provided by doctors who are “in network” and less for doctors who are “out of network.” Those patients are the ones receiving exorbitant bills from S.F. General, which is always “out of network.”

Kagan said the issue affected just 300 patients last year and that, moving forward, the hospital will do a better job warning patients they may receive large bills, which she acknowledged can be “stressful and upsetting.”

Kagan said the hospital is also trying to figure out if there are “other policy changes we could work with the city on or we could also just determine ourselves with our billing practices.”

Supervisor Aaron Peskin has called for a hearing on the matter, a move supported by Supervisors Rafael Mandelman, Catherine Stefani and Hillary Ronen. He said the charges approved by the supervisors and mayor are high, but appear to be in line with other hospitals.

“The issue is a patchwork health care system that creates these relatively rare situations where patients can be left holding the bag,” he said. “It definitely needs to be fixed.”

Breed agrees, calling the current situation “problematic.” She said she’s close to naming a new chief of the Department of Public Health after former Director Barbara Garcia was forced to resign amid allegations she steered city contracts to her wife’s workplace.

“I am hopeful this is one of the charges they will take on,” Breed said of the billing mess. (Note to the mayor: You’re hiring this person. You can demand it.)

Breed recalled being in her late 20s and participating in a ropes course at Lake Tahoe.

“I fell out of a tree and fractured my vertebrae,” she said. Breed was a Kaiser member, but there was no Kaiser hospital nearby. But despite being treated at a non-Kaiser hospital, she was charged a regular co-pay, and Kaiser covered the rest.

“That’s how it should be,” she said.

Assemblyman David Chiu said he’s researching solutions at the state level, but warned the ban on balance billing for HMO patients took years, so there will be no quick fix.

“It’s completely egregious,” Chiu, D-San Francisco, said of the current setup. “The hospital wants insured patients to pay a little more to cover the costs of uninsured patients, but bills of tens of thousands of dollars is not paying a little more. It’s just not fair.”

There’s a seemingly easy fix: Get what you can from the insurance company, and forgive the rest. That’s what S.F. General does for patients insured by HMOs because state law requires it. Why not do it for everybody?

Don’t spend months or years of hospital billing agents’ time on back-and-forth phone calls with unwitting patients. Don’t send bills to collection agents for even more rigmarole. Don’t make the billing experience more painful than the physical trauma that prompted it.

“That would seem to be the fair thing to do,” Chiu agreed.

If this really affects just 300 people a year, it won’t make that much difference to the hospital’s bottom line. But it could make all the difference to the person who, on one terrible day, ended up at S.F. General.

San Francisco Chronicle columnist Heather Knight appears Sundays and Tuesdays. Email: hknight@sfchronicle.com Twitter: @hknightsf