YC talks aren't recorded, for similar reasons. When you know every word you say will be potential fodder for a sensationalist news story, it's harder to be blunt about what went right and wrong.
Especially when the narrative people want to spin is "Gee golly whiz look at those Silicon Valley folks saving the day!".
Anything else is CYOA, and it'd be nice if people could actually rise to the occasion and be honest and precise.
(Besides, if you are honest on everything, and somebody just hits you out of context, you can defend yourself by providing additional context. None of this is going to matter in 5 years anyways, so might as well set a good example.)
I don't think so. The people fixing the obamacare website most likely want obamacare to succeed, and are aware that there's a hungry media out there ready and waiting for the next story revealing just how awful the original website (and, they'll insinuate, hence obamacare itself) is.
I can write down an out-of-context statement and report it with or without a recording. If anything, a recording is positive because you can contest what I claim you said with a hard-to-fake, in-context version of things.