This is basically correct. If the check is from that particular bank they can easily call the person who wrote it and ask "did you write this check?". But no one would do that for a deposit. If you work at a bank you can recognize your own checks just by looking at them.

If the check is for a different bank and looks really fake, a bank might not deposit it and ask some questions about it ("who gave it to you?"). This is to protect depositors from fake check scams ("deposit this check and give me back 10%"). If the person really wanted to deposit it, the bank employees might recommend cashing it at the bank listed on the check. They will know if it's real.

I actually saw a similar situation to the one here. A black non-customer had a large denomination check that looked different from normal checks. After some questions, he said he got it from a settlement. It turned out that the check was fine, the check design was just not used often. Total time was like 20 minutes to verify the check, open the account, and deposit it. He said he would bring his next settlement check next time.

See? Easy to verify it and not be racist.