In Degeneration, Leon is shown 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.
This would explain her work with Terra Save in Revelations 2...
While the whole "chosen to be pacifist" thing is a very good natured choice in most situations, it's a goddamn outbreak! she took down several zombies in seconds while holding a small child with a few well placed shots and a kick, the whole "I don't want to use a gun" argument doesn't hold water when the other option is a bunch of rotting former humans with a hankering for human flesh munching your face off. Its the same thing with barrys daughter in revelations, while true she has a problem with guns due to the accident (read RE:R2 for the accident) not having a firearm in a situation with monsters is just plain stupid, i'd have taken my spare gun handed it to her and just went "listen, save the whole non-combatant crap for when we aren't about to be eaten."
A) Nobody cares what you would've done in that situation.
B) She's focused on taking care of Rani, not kicking ass, and taking care of Rani doesn't require a gun. Claire would've made it out of the airport without firing a shot if not for the senator.