@James Halliday: "the point of parody"
"The point of a parody is that the audience knows it's a parody." Very true.
But the short reply is: you've heard of Trolls, right? Ask serious but stupid question, get passionate/didactic answers? Other straight-faced humour?
Elaborating, (a) a good parody can start believably and stray into the deeply surreal --- so that the audience only finds out after a while, and starts to question when/where it crossed a line. So in a press conference this may be at the Questions/Answers for all I care, leaving a quick-filing hack caught out.
But crucially here to your remark, (b) the audience is not the handful of stuffed shirts impersonated nor the attending journos, but those tens (hundreds) of thousands (most extra, 'coz this DMCA notice) arriving to the Yes Men site or movie --- all those understand it's a spoof. In their movie for example, they convince a business audience that the case for slavery is a strong one (see also under: Swift, J. "a modest proposal"). No admittance of parody, but the viewer knows.
And the other way around, e.g. the "peanut butter refutes evolution" [e.g. http://www.youtube.com/watch?v=FZFG5PKw504&NR=1 ] argument is completely hilarious from second one and obviously nonsense, and makes you think where the strawman is inserted etc; however it's not a parody as the reverend is serious and several re-posters support every sentence in it.
Essentially, requesting a DMCA takedown places them at the gun/foot interface.