The fight over Bain Capital is heating up. 

Former Massachusetts governor Mitt Romney’s campaign manager Matt Rhoades is calling on the president to apologize for his own staff for “a reckless and unsubstantiated charge” that Romney lied about when he left the private venture firm. Rhodes said the charge is “so over the top that it calls into question the integrity of their entire campaign.”

It’s the latest bit of nastiness in an increasingly nasty campaign over Romney’s business career — a career Obama’s campaign has tried to turn into an albatross.

Obama deputy campaign manager Stephanie Cutter, along with Obama campaign lawyer Bob Bauer, argued Thursday that Romney may have lied to the Securities and Exchange Commission about leaving Bain in early 1999 to run the Salt Lake City Olympics.

Their accusations were based on a Boston Globe story reporting that SEC filings show Romney remained chief executive, chairman, and sole stockholder at Bain through 2002. The documents also showed, according to the Globe, that Romney earned $100,000 as a Bain “executive” in 2001 and 2002.

The date is important, because Romney argues that he isn’t responsible for the outsourcing, job losses and bad deals that Bain had a hand in after 1999 — he was busy running the Olympics. Thus, ads focused on anything that happened at Bain post-1999 are untrue.

Cutter told reporters that Romney is the liar, either “misrepresenting his own position at Bain to the SEC, which is a felony, or he was misrepresenting his position at Bain to the American people.”

Bauer added that if Romney “was not the controlling person that is described [in the filings], that means that these statements are false and ... there are very, very serious legal consequences that would follow.”

Cutter had a message directly aimed at Romney: “If the SEC filings aren’t accurate, prove it ... Prove it by releasing your tax returns.” (Goading Romney into releasing those returns, or at least keeping his refusal to do so in the spotlight, could easily by the Obama campaign’s real goal here — more than defending their own ads.)

Though Rhoades was not specific, it is presumably the felony accusations he refers to in his statement.

“President Obama ought to apologize for the out-of-control behavior of his staff, which demeans the office he holds,” Rhoades wrote. “Campaigns are supposed to be hard fought, but statements like those made by Stephanie Cutter belittle the process and the candidate on whose behalf she works.”

The aggressive statement goes along with a newly combative Romney campaign; earlier in the day the candidate released an ad calling Obama a president you can’t trust.

Our Factchecker has dismissed the Globe report, explaining that while Romney “had not legally separated from Bain,” by virtually every account he was a “passive investor” with no managerial role in the firm after leaving for Salt Lake City.

Fortune magazine has also found documents showing that Romney was not listed among investment fund management in 2000 and 2001.

And in a statement, Bain Capital said Romney “has had absolutely no involvement with the management or investment activities of the firm” since leaving to run the Olympics, but that “due to the sudden nature” of his depature, he remained the sole stockholder for some time and his name was on SEC filings “in various capacities.”

But Obama’s campaign has continued to press the point. Bauer hinted that the campaign had some proof that Romney was not just invested in Bain but involved in decisions after 1999. “I would stay very much tuned on that,” he said.

Of course, if Obama’s campaign has some such smoking gun, it’s hard to imagine that they would keep it hidden very long. Whoever comes out on top in this fight, one this is clear — we were right when we called this week the “Real World” moment of 2012.

This story has been updated.