I recall being asked on a job application whether I was ever arrested, regardless of conviction. In some places, mere involvement with law enforcement is taboo.
Would it be possible to verify if you lied answering that question?
Possible but costly. The US lacks a single information system regarding criminal history. There are private investigators, other private companies in the business of "record retrieval", but the results are not 100% accurate.
...and google. Many arrest records seem to be published online in the US.
Maybe not right away, but 5 years down the road when you're in an ugly power struggle with some other jerk for a middle management position HR might get an anonymous tip about how you lied on your resume.