reality: get the equity, get out, get an exit
the incongruences in your resume won't matter, the number of vacation days you took compared to someone else won't matter, the number of hours you stayed late won't matter
solve the inefficiencies in the hiring process if it bothers you
By your logic, if someone is doing their job satisfactorily, but they hid several major felonies (say armed robbery, and robbing from their prior employer) from you during the interview process, you wouldn't fire them?
I'd rather have someone have the courage to own up to their issues. If they don't in the interview process, they won't later. And I like to hire folks who have something to prove. But not folks who overtly lie.
But in this case you're firing them for being honest and not keeping up the lie.
You'd be sending a signal to all your staff that they better keep lying.