In Degeneration, Leon is shown to be extremely Genre Savvy and to ignore standard procedure in favor of what works. So why is Claire, who is more experienced and probably a better shot than the two squad members with him, not immediately given a gun?
She doesn't want one. When Leon throws her his pistol in the airport, she gives it back to him as soon as she can.
We're given the impression that since Code: Veronica, Claire simply hasn't been in combat—so she's hardly going to be "more experienced and probably a better shot" than two career soldiers, except inasmuch as she's dealt with zombies before. In any case, Claire's deliberately and consciously taken on the role of a healer and caretaker more than a fighter. She'll fight when she has to, but prefers not to.