There are legal implications to exempt vs. non-exempt employment.
As one poster already mentioned, start tracking an exempt person's time on the clock and they can claim to be non-exempt in function then it is a fight over them being owed OT for hours worked over 40, they were have not been compensated for.
As yet another poster already mentioned, if you are exempt it does not matter if it takes you more than 40 hours to do the work - you work over and get paid the same.
The relevant regulations are the FLSA and the classification of jobs
Special rules do apply to exempt employees especially about arrival to work.
In a broad over generalization people responsible for managing people are exempt with rare exceptions.
As far as your concerns regarding a person being at work, do you not have security ID scans or computer log-on times that can be utilized to determine if the person were at work a particular day?