I’m not sure if anyone still cares, but after noodling over this a bit I think I’m basically convinced by the Atrios/Salmon/Yglesias argument that there’s some real benefit to government briefing sessions that don’t allow direct quotes. Spin will be a big part of these sessions regardless, and if this rule allows government officials to talk like real people instead of worrying that the slightest misstep will produce some headline-worthy gaffe, then it’s probably a useful thing. Felix makes the case pretty well here.
On the other hand, the argument for not being able to attribute your paraphrases to specific officials still seems pretty dodgy. On balance, then, I say: paraphrase rule yes, ID rule no.