Emily wrote:
You misunderstood. They claimed this was because of the TSA rule.
Clearly, the rule doesn't apply to rentals.

Today even the person behind the counter at the FBO is required to take
TSA training. In that training they spend a lot of time talking about
the risks of new renters. They give yuo several scenarios and ask you
how do you react. After sitting through all that training I could
easily see how an FBO would be concerned enough to ask for
documentation for all renters. TSA is basically saying the person
behind the counter is responsible for determining if a new renter is a
terrorist or not.