There is no single standard for "fair use." It's up to a judge to decide, this is why it's so problematic in the USA.
One judge in one district will say it IS fair use, while another will say a virtually idental case ISN'T fair use.
I run a few parody websites, I always get DMCA notices and lawsuit threats. I simply remind them, it's "fair use," and I'd be more than happy to discuss it with them in front of a judge. Of course if I win, you'll have to pay my court costs and such, and if YOU WIN, I have nothing so you'll have essentially wasted your time.
So far <knock wood> it's always worked.
Remember in America lawsuits are not about right/wrong. They are about having enough money to keep suing the other guy till he gives up.