That's not true at all. Overtime can most definitely be unpaid, and usually is.

By the legal definition, sure, but in common usage the word "overtime" is usually qualified as "unpaid overtime" if that's the case.

Invoking the word "overtime" to mean "unpaid overtime," especially by young team-members, typically results in uncomfortable coughs, silence, and expectation setting from managers / senior members of the team, none of which would be necessary if, like the word "crunch," the unqualified word carried no connotation of payment. I've seen this happen many times in a number of settings so I'm pretty sure it's not just a regional quirk. Connotations are important.

No one I know specifies overtime as unpaid or paid. It is simply time that is worked over the amount normally worked, and may be paid or not.

Of my friends, I know if some of them say they worked overtime they mean unpaid, and I know if some of them say they worked overtime they're getting a fat paycheque.

Legal reference? (This is a matter of law, re engineer's compensation.)

and couldn't crunch also be paid?

Unless you are "Salary Exempt," in the which case overtime is not paid.