I have a co-worker (who is now a short timer with a week to go), who claims that since he is salaried and exempt that it is against the law in PA for our employer to track his hours. If he is at work for at least an hour a day, that is sufficient for him to be able to claim that he worked on that day. Our employer requires us to submit a time sheet each pay period with the amount of time spent working, on vacation or on personal time.
His theory makes no sense to me. He sounds mistaken to me (even though I would love it to be true, it sounds like nonsense).

It is nonsense. An exempt employee is no more entitled to come and go as they please than a non-exempt employee. And there are some entirely valid reasons for an exempt employee to have their time tracked; client billing, for benefits that are hours-based such as 401k's and FMLA, suspicion of abuse, even safety in some cases (knowing instantly who is and is not in the building in case of fire, etc.). NO state prohibits an employer from tracking the hours of an exempt employee, and if an exempt employee is not working the hours the employer thinks they should be, the employee can be disciplined or fired.

However, he is correct that if he works any part of the day, he has to be paid for the entire day (barring absences related to FMLA). He can be disciplined for only working an hour a day and he can have his vacation time docked to cover the rest. But he can't have his pay docked if he works any part of the day at all.