This feels a bit anticipatory.
I understand the pain point - both the player and the Ref not having skill in medicine and yet making calls regarding whether or not medical tools are required to perform a given medical task. But HAS the player tried to perform brain surgery in a swamp with naught but sticks? It doesn't sound like it. It sounds as though the player asked if they could treat a critical arm injury without medical equipment, which should just be a Ref call. As a rhetorical question/thought exercise, if you're wrong and the players don't call you out for being wrong because they also don't have the necessary level of medical knowledge, then does it ultimately matter?
I agree that this should probably just be resolved by the Ref making a call regarding whether or not an action can be undertaken with the equipment supplies at hand in a narrative sense, and if it can't or if the players don't have the required equipment, then a penalty modifier should probably be applied. If a given action/roll is causing that much consternation, then perhaps some research can be done prior to the next session in order to make a more informed call.
Well, in the end my ruling was that "yes, you have to use a medical kit to fix a critical injury on an arm from gunfire".
And I've decided that if you're gonna use your medical skill for injuries, you need to use a medkit, or you'll get a negative modifier.
Because if the players don't, you take away another layer of scarcity for the game.
"Oh you don't have any medkits?"
"That's ok, because you still have a 96% chance to fix *any* critical injury according to RAW."
So no, in my game, you have to use medkits or other medical equipment.
Keep in mind that there is more medical equipment than just single-use medkits, and these become more important now.
Since I'm using an expanded loot list, I also had the opportunity to add different types of trauma kits that can be used more than once as well as plenty of other medical equipment.
So, now my players have started actively looking for medical equipment for future use.
(Before that, some of them were even discussing trading away medkits since they were "useless" due to the medic(s) having an almost 100% chance of fixing pretty much any injury without any medical equpment.)
This is a *very* rules-light game and I feel that some house-ruling is needed on occasion to stop players from just ignoring certain equipment and difficulties.