If that were true, it would be an incredibly costly way to spread FUD, with an almost negligible impact in the end!! I can come up with at least a dozen more effective ways to spread FUD if someone were truly willing to invest that much money.
My belief goes to their belief in mining pools that won't enjoy those bitcoin. If a mining pool is greedy and take it, that mining pool will be criticized by community and I did not check but some mistakenly transactions like this one, only went to big mining pools.
But still, that would be too much of a gamble. Over 2% of all blocks each month are mined by solo miners or obscure mining pools that are unknown to the public. If there's no one to point fingers at, the community wouldn't have anyone to criticize.
I wonder if F2Pool stated how exactly is the unlucky sender supposed to make a claim. I wouldn't be surprised if they got flooded with spam messages from either jokers or scammers pretending to be the sender, so it might take some time to weed out the fake ones and verify the real one.
Regardless of the communication method, I'm confident that the folks at F2Pool are smart enough to know the only surefire way to prove address ownership. We're in the crypto world, after all.