Here's a not-so-comforting lesson for investors, courtesy of the Securities and Exchange Commission. Just because the SEC says a company's earnings were fraudulent doesn't mean the company will ever be required to correct them.

The SEC this week accused Fifth Third Bancorp of committing accounting fraud during the height of the 2008 financial crisis. The company agreed to pay a $6.5 million penalty to settle the agency's claims.

The funny part: Fifth Third, which is Ohio's largest bank, has never acknowledged to this day that its numbers were in error. The SEC isn't requiring it to do so now. A Fifth Third spokesman, Larry Magnesen, said the company considered whether it needed to do a financial restatement and decided it didn't.

Reasonable people might disagree about whether Fifth Third committed fraud. Per the usual protocol, Fifth Third neither admitted nor denied the SEC's allegations. Yet it's beyond belief that the company never had to set the record straight about its financial statements. Fifth Third first disclosed the SEC's investigation in its 2010 annual report. So the bank has had a few years to revise its figures.

Surely an accounting error that is fraudulent also should be deemed material by SEC. Yet the agency isn't treating it that way. An SEC spokesman, John Nester, declined to comment.

According to the SEC's Dec. 4 administrative order, Fifth Third's loss for the third quarter of 2008 would have been more than twice what it reported, had it complied with generally accepted accounting principles. The bank had been trying to sell some troubled commercial real-estate loans that had plunged in value. However, it continued to classify the loans as "held for investment" instead of "held for sale." This let the bank avoid a $169 million writedown that quarter. Fifth Third reclassified the loans the following quarter. It sold most of the loans at issue in December 2008 and in 2009.

The SEC in its order said Fifth Third and its chief financial officer at the time, Daniel Poston, violated federal antifraud laws. (Poston, who will pay $100,000, also got a neither-admit-nor-deny deal.) Comment letters to the company from the SEC's staff show the agency was asking Fifth Third about its loan accounting as far back as May 2010.

"It appears that the company should have restated in 2010," says Don Whalen, general counsel and research director at Sutton, Massachusetts-based Audit Analytics, which tracks restatement data.

If nothing else, the Fifth Third case may help explain why restatements by U.S. banks declined after the financial crisis got started. Back in March 2011, I wrote a column that noted there were 133 banks that issued corrections from 2008 through 2010, according to Audit Analytics. That was down from 169 banks during the previous three-year period, before the crisis took off in earnest. That made no sense, considering the country had just experienced the greatest banking-industry meltdown since the Great Depression. The obvious conclusion was that the government had given lots of banks a free pass.

In at least this one instance, the SEC identified GAAP violations so egregious that they amounted to fraud -- and never required a correction. Perhaps the moral of this story is that if a company drags out an accounting investigation long enough, it won't have to admit any mistakes, because by then the matter will be ancient history.

(Jonathan Weil is a Bloomberg View columnist. Follow him on Twitter.)