The logic is impeccable: why do we search pilots when they get (access to) a gun once they have been cleared.
The reason they search pilots is because the only obvious things distinguishing a pilot from a non-pilot are a fancy uniform and an ID. If pilots are exempt from screening, then your method of determining who is a pilot needs to be at least as effective as the screening itself. Otherwise, an adversary needs only to steal or forge the proper credentials to bypass screening.
Either Paul is aware of this and is being deliberately misleading to make his case, or he hasn't given the issue enough consideration.