WARNING: EXTREME RULES PEDANTRY AHEAD
My point is that, by my understanding of the rules, using your Mental Traits for gun combat does not change the fact that shooting someone is a Physical Challenge. If it were a Mental Challenge, the shooter would be comparing their Mental Traits to the target's Mental Traits in the event of a tie, right? Normally, according to Initial Bid; LotW rev pg. 167: "Most challenges are categorized as Physical, Social or Mental, and all Traits used in a challenge must be from the same category. Experienced players may offer each other more creative leeway, but only by mutual agreement."
Now, when someone attacks with a gun using Mental Traits, their target who is trying to dodge compares Physical Traits with them in the case of a tie. By the above rule, all Traits used in a challenge must be from the same category. Now, as Tom correctly points out, specific exceptions trump general rules, so either this is a Physical Challenge but the attacker can bid Mental Traits because of a specific rule, or this is a Mental Challenge and the defender can bid Physical Traits because of a specific rule. There is a specific rule which allows the bidding of Mental Traits for gun combat. There is no specific rule which allows for the use of Physical Traits to defend in a Mental Challenge (well, at least none that would have been at play in the situation described). Therefore, to my mind, shooting people is a Physical Challenge, and the challenger is allowed to bid Mental Traits in it due to a special rule.
If we assume that attacks with Firearms are Mental Challenges, and thus can be used after being Falling Touched, we end up with the weird edge case in which shooting someone is totally doable but throwing things (via Athletics or Throwing) is not. I guess throwing things is marginally harder? Point is, my understanding of Falling Touch, flavor-wise, was always that it was basically spiritually-enhanced nerve disruption. That's why the retest is Medicine. This nerve disruption prevents people from mustering the coordination to attack or stand, but they can still roll out of the way of attacks. Mental attacks with no physical component (e.g., Hand of the Earth Lords) would also still be doable.
Anyway, this is my interpretation. As I'm the newest and least experienced Staff Member, I don't know that it should be the "official" rule on how Falling Touch works at RAtC, but clearly it's something that we should standardize explicitly, as I (at least) do care that it's run consistently from scene to scene. I think I can confidently speak for the rest of Staff in saying that the rule of thumb isn't going to be "Someone falling touch Tom again? Yeah he's fucked."
Does anyone remember past scenes at RAtC wherein people were Falling Touched but could still shoot by bidding Mental Traits? Precedent is helpful.