Edit: upon further reflection, I wonder if the problem is simply that the fake checks are copying legitimate bank accounts and the fraud is not discovered until the real owner of the account realizes that there was a deduction from their account for a check they didn’t write? I suppose that if I had played along further I would have a better understanding of the details about how these frauds work, but it’s obviously not worth the aggravation.
This is technically the only accurate definition of a "fake" check. I can hand write a check to you on a napkin and as long as its formatted correctly and has the proper account and routing number it's a legitimate check that can be deposited. The security features of modern printed checks are completely optional and mostly just speed up processing. That's why printing your own checks at home is a completely legitimate option.
If you want to hedge your bets at all when dealing with a check, you can call the institution the check is written against and verify that the account has the funds on deposit to cover it and verify that the person on the account is the person writing the check. That's about all you have and I'm sure there are ways around that too.
Personally, I find checks to be completely archaic and I often go many years between writing them and I've only accepted them from friends/family for stuff like group buys to split shipping costs on stuff. I'd never take a check from a stranger, period. If they can't get it together enough to turn their own check into cash before we meet, I don't need to sell them my stuff.