Brad DeLong and other commentators seem to have an unnecessary need to prove that Fannie and Freddie's hands were clean with respect to the credit crisis. The Republican narrative about the mortgage crisis originating with government forcing lenders to loan to unqualified minorities is indeed a bunch of nonsense; the volume of those programs never amounted to anything and subprime borrowers had no particular racial skew. However, Freddie and Fannie played a significant role in the mortgage crisis because they enabled the market bubble to grow so big.
Fannie and Freddie are $5 trillion dollars worth of the mortgage market. Their "implicit government guarantee" allowed them to operate at 200:1 leverage ratios, which blew up when not only their subprime portfolio did, but also when their conforming mortgages delinquency skyrocketed. Fannie and Freddie bought hundreds of billions worth of subprime and Alt-A-backed securities, which made them a big part of the market for Wall Street to sell their CDO sausages to.
Now, to their credit, the GSEs never touched the most egregious loans like no-docs, "liar loans", and the like that raged at the top of the bubble. That stuff was the true toxic waste. But the fact is, the GSEs are in conservatorship right now, pushing losses of tens of billions of dollars a quarter onto the taxpayer, because they took on too much risk with too little capital buffers. That is what caused this crisis, and Fannie and Freddie definitely contributed to the problem.