Quantifying the revolving door is difficult—it involves a series of subjective choices about what constitutes the revolving door, what level of employees should be counted, and so on. (One study from Notre Dame found a double-digit increase between 2001 and 2013.) But there's ample anecdotal evidence. In fact, Bernanke isn't even the first Federal Reserve alum to jump to a hedge fund in the last month. Jeremy Stein, a former governor, was hired by BlueMountain Capital Management in late March. And as Rob Copeland notes, this is just the latest in a stream of prominent government officials:

Former Federal Reserve chairman Alan Greenspan and ex-Reagan economic adviser Martin Feldstein accepted paid roles on a now-disbanded economic advisory board at John Paulson’s hedge-fund firm that started in 2008. More recently, former Obama administration chief of staff William Daley joined Swiss hedge fund Argentiere Capital, while former Treasury Secretary Timothy Geithner and former Central Intelligence Agency chief David Petraeus took posts at private-equity firms Warburg Pincus LLC and KKR, respectively.

And just this week, former Massachusetts governor Deval Patrick was introduced as a new managing director at Bain Capital.

That doesn't even include non-hedge-fund and private-equity moves. Peter Orszag, who led President Obama's Office of Management and Budget, took a job with Citigroup when he left. The Obama administration had been closely involved with Citi in the aftermath of the financial collapse, and the bank received nearly $500 billion in bailouts. Orszag is not allowed to deal with the federal government directly, but as The Times noted, perhaps wryly, "Mr. Orszag’s actual duties are murky at best. He is expected to draw on his deep knowledge of public sector financial issues and his experience overseeing the federal budget to counsel Citi’s clients on various policy actions."

The thing about Bernanke's announcement is that he appears to be conscious of how bad it looks. “I wanted to avoid the appearance of a conflict of interest,” he said. “I ruled out any firm that was regulated by the Federal Reserve.”

That's true. But many people argued that hedge funds contributed to the systemic risks that helped bring about the financial collapse—which is one reason that hedge funds and private equity are covered by the Volcker Rule in the Dodd-Frank financial-reform legislation. In fact, it is the Federal Reserve that's overseeing the process of big banks extricating themselves from hedge funds. Besides, given that many people worry that the financial sector is under-regulated, the reminder may not be much of a comfort. Back in 2006, one Ben Bernanke gave a speech grappling with the growing systemic risks of hedge funds.

Meanwhile, Bernanke has many other ways to influence business, even outside of any direct regulatory conflicts of interest. As the anecdote about the trader shows, Bernanke's casual remarks can move markets, and he also delivers speeches and other remarks—in fact, through his post as a full-time fellow at the Brookings Institution, he recently started blogging.

Perhaps what makes Bernanke's case so worrisome is that he has an almost universal reputation for probity. If the revolving-door system is so powerful that it can make even him look suspect, is it beyond redemption?