The mistake being, what, accidentally sneezing onto the printscreen button so hard it depresses?

This isn't the same as leaving a tool in someone; making and misplacing a screencap take active doing. If your meeting participants actively want to put data where it doesn't belong, the solution isn't accident prevention

The mistake being to intentionally take a copy of something confidential, because you forgot it was supposed to be confidential. People do things like this all the time.

It's essentially a guardrail. It can be easily circumvented if someone was being actively malicious.