You might be a bit optimistic here: it's not always easy to deal with "lying false positives". Depending on the
legislation it may be difficult to fire somebody, and involve going to court, sometimes going on over several years.
Vindictive personalities may engage in sabotaging the company, the team, their (former) co-workers, as
a retaliation for being fired.
(Anecdote: I have witnessed all of the above in my work.)
Summary: the cost of a false positive almost always outweighs the cost of a false negative.
I don't think there's any state in the US where lying on your resume/CV is not legal grounds for immediate termination.
And any company that has thought about their hiring process for more than 30 minutes will have a probationary period of 30 or 60 days or so, after which employment can be terminated if the employee is not able to do the work.
Are you not in the US? I've never ever come across such a thing - probably because US companies can theoretically fire you on the spot for almost any reason except specifically disallowed discrimination, and most definitely for being unable to do the work.
Summary: the cost of a false positive almost always outweighs the cost of a false negative.