A Federal Reserve official said this week that "banks are still not lending." He also said access to credit remains difficult for households and small businesses. That part is true. The first statement is not.

Here's what was said, from Moneynews:

Despite a more stable financial system, banks are still not lending and the quality of loans on their books continues to get worse as the U.S. housing market remains in the doldrums, a top official at the Federal Reserve said on Wednesday.

"Access to credit also remains difficult, especially for households and small businesses that depend significantly on banks for financing," said Jon Greenlee, Associate Director for Bank Supervision and Regulation at the Fed.

Ah, but banks are lending -- lots and lots of money. Not to households and small businesses, but to the same entity that is providing the money to lend. The government.

Marketplace Senior editor Paddy Hirsch explains in his latest Whiteboard video: How the big banks make the big bucks.

One thing in Paddy's excellent explanation that I must quibble with: He says banks are borrowing from the Fed at practically zero interest, then lending it to the Treasury by purchasing government bonds, and collecting the interest at maturity. But he uses the example of a 5% interest rate. Rates on one-year T-bills are nowhere near that. They're about a third of a percent. I doubt banks are raking in the dough that way. More likely, they are buying long-term bonds to keep on their books and/or foreign bonds from emerging economies that are paying higher interest. Either way, and I know this sounds counterintuitive, but banks are exposing themselves. Reuters explains:

Historically, banks' risk models have tended to assume that the bonds of developed countries were close to risk-free assets. No longer. The government finances of peripheral countries such as Greece and Ireland are already creaking. And many investors believe it is only a matter of time before ratings agencies lower the UK's credit rating. A downgrade -- or, heaven forbid, a default -- could leave banks exposed.

"Banks are filling their books with long-dated government paper, funded with short-term government funding," said a senior executive at a large UK-based bank, who asked not to be named. "It's the biggest carry trade in the world."

Banks are also taking the free money from the Fed and turning profits in the securities markets. There again, the banks are increasing their risk:

Analysts at FBR Capital Markets estimate that up to 40 percent of investment banking revenue over the last 12 months has come from banks trading with their own funds, compared with a more typical level of about 25 percent.

All of the top U.S. banks have reported rising value-at-risk levels, signaling that their biggest trading loss on most days is rising.

Take Goldman Sachs, for example. Its biggest possible loss on 95 percent of the trading days in 2009 was $218 million, compared with $180 million for 2008. For JPMorgan Chase the largest possible loss for 99 percent of its trading days in 2009 was $248 million, compared with $202 million.

So while the banks seem to be getting a sweet deal from the government right now, they'd better be careful. Buying government bonds is a way for them to reduce the riskiness of their balance sheets, historically. But we've never been here before -- the trillions being borrowed by these governments. And if the banks are increasing their risk elsewhere, like in securities, what happens if the market crashes again? Despite the sense that government would step in, there won't be (and shouldn't be) any refuge left to offer.