(CNN) Prosecutors said Friday that they misunderstood text messages used as the basis of a claim that Maria Butina offered to trade sex for access -- an extraordinary admission that threatens to undercut the government's cloak-and-dagger portrayal of the young Russian accused of working to infiltrate American political circles.

The government made the explosive allegation that Butina offered "sex in exchange for a position within a special interest organization" in a filing in July -- a claim that has been hotly disputed by her lawyer.

"I want the government's walk back to get as much coverage, as prominently, as their initial false allegation," said Robert Driscoll, Butina's attorney.

The government acknowledged its error in a filing released just before midnight Friday but said there was still reason to question the depth of Butina's commitment to her boyfriend, Paul Erickson. Erickson is a South Dakota conservative political operative who CNN has identified as "U.S. Person 1" in government filings. He has not been charged with any wrongdoing.

"Even granting that the government's understanding of this particular text conversation was mistaken, other communications and materials in the government's possession (and produced to the defense) call into doubt the defendant's claim that her relationship with U.S. Person 1 is a sufficiently strong tie to ensure her appearance in court to face the charges against her if she is released," according to the government's filing.

Butina has pleaded not guilty to charges that she was acting as an agent for the Russian government since her arrest in July. The about face by the government will likely take away little from the central case against Butina, which is bolstered by extensive communications she exchanged with her mentor, a Kremlin-linked banker, and meetings she had with officials from the National Rifle Association.

But the admission represents a victory for Butina's defense team, which has attempted to soften the 29-year-old's image and win her release from jail.

The accusation first made its way into the public eye eight pages into a July filing from the government that argued Butina was a flight risk and should be detained before trial.

"On at least one occasion, Butina offered an individual other than U.S. Person 1 sex in exchange for a position within a special interest organization," prosecutors wrote in that filing, saying it supported the notion that her years-long relationship with Erickson was not legitimate, and merely cover that did "not represent a strong tie to the United States" that would prevent her from fleeing.

The detail quickly jumped to newspaper headlines and cable news banners, and drew a rebuke from Butina's attorney, who demanded in interviews and in federal court that the government offer up their evidence behind the claim.

Butina's initial request to be released from custody was denied by a federal judge in July.

"The impact of this inflammatory allegation, which painted Ms. Butina as some type of Kremlin-trained seductress, or spy-novel honeypot character, trading sex for access and power, cannot be overstated," Driscoll wrote in court documents last month.

By August, the messages relied on by the prosecutors to make the assertion were "eventually produced" to Driscoll, he wrote in a filing, and it "does nothing to support the government's claim."

"The only evidence the government relied on for its explosive claim was an excerpt from an innocuous three-year-old text exchange" sent while in Russia between Butina and a "longtime friend" who ran public relations for the gun rights group she founded, Driscoll said.

After taking Butina's car for an insurance inspection, the man, referred to by his initials, DK, texted Butina, "I don't know what you owe me for this insurance they put me through the wringer," according to the filing.

"Sex. Thank you so much. I have nothing else at all. Not a nickel to my name," Butina replied -- "jokingly" -- her attorney wrote.

Butina later wrote that DK could "ask for anything," adding, "That they hire you?"

The message was a taunt, meant as a "good-humored reminder that he already works for her gun rights organization, as well as advertising agency," Driscoll wrote, demanding that prosecutors withdraw or strike the accusation.

On Friday, prosecutors wrote that their charge that Butina offered to trade sex was based both on a series of text messages with DK "and other information about the relationship between the defendant and DK gained through a review of additional communications between them," though they did not outline any new exchanges.

They added that the one exchange they had misunderstood was not the only piece of evidence undergirding their belief that the relationship would not prevent her from fleeing and said that Butina had also offered to "provide information to the government" in a separate and ongoing fraud case involving Erickson. Erickson has not responded to CNN's request for comment on the fraud allegations.

Butina has also messaged friends about the dating app Tinder and once wrote "let's go have fun with guys," according to court filings.

Prosecutors wrote in the filing that Russian government officials have made six consular visits to Butina while she is behind bars, and the Russian foreign minister has complained about the case on two occasions to US Secretary of State Mike Pompeo — actions that "confirmed her relationship with, and value to, her own government."

Responding late Sunday to the filing, Butina's attorneys slammed the government for "shamelessly [admitting] it had no factual basis" for the claim and said none of the other evidence that the government said it had bears "any relevance to the initial claim that Maria offered to trade sex for access and power."

"The government's documents do nothing to discredit the sincerity of her relationship with Paul Erickson, and its craze with her sex life has gone too far and transformed into an irrelevant obsession," they wrote.

The defense team on Sunday also alleged that the government had tried to sneak another correction into their Friday filing -- acknowledging that Butina had actually received a type of work visa after her student visa elapsed, not just a tourist visa as the government previously claimed. The government said the mistake was just in the labeling of the visa program, but Butina's defense said the fact "carries a very different implication about her future plans in the United States and undermines the government's fear of her bolting to Russia."

The admissions come amid a separate fight that has hung over the case for weeks -- a proposed gag order that prosecutors want to prevent Butina's attorney from speaking with the press in a way they say could prejudice a jury.

Butina's supporters have in recent weeks taken steps to shift the light in which she is portrayed. A new fundraising website splashes a headshot of Butina smiling over a white and pink background along with the words: "I'm Maria, and I need your help."

And late last month, ABC News obtained a heavily-produced video of Butina and her boyfriend performing a duet of a love song from the Disney movie "Beauty and the Beast," which Driscoll, her lawyer, said underscored the extent of their relationship.

"Having successfully created a false media narrative that this case is more about Maria Butina seducing NRA members and Republicans than its gossamer-thin evidence that Maria was acting on anyone's behalf other than her own, the government now seeks to prevent her and her counsel from even attempting to correct the public record," Butina's attorney wrote in a filing Friday.

Both sides are expected back in court Monday afternoon for a status conference.