If someone lies that their password was stolen to hide them being the originator of a single email, who are they telling the lie? Is it a court? In many cases the person would be caught through behavioral analysis. They didn't change their password, so it wasn't really stolen. No other emails were improperly authored, so it wasn't really stolen. They never reported it to the email server owner, so it wasn't really stolen.

Lying isn't a stronger defense to perform abuse than weak keys are for stopping abuse.