So, how would either of us judge whether something is possible or not?
Well first of all remember, that the critical hits themselves are not written in stone. The referee is supposed to color and determine the damage based on the actual thing that caused it. Only the mechanical effects are the same. Take example of military grade barbed wire: moving across it and failing gives automatic critical roll to legs. A player has a bad day and he rolls a 10: Severed leg.
Really? Like he stumbled on the wire and in panic tore off his own leg? The barbs biting through bone and sinew all the way? Probably not. Probably something else, yet as severe, happened.
So you will probably describe just how his leg is so tangled in the wire that is biting through it and causing severe bleeding and permanent nerve damage. (And tbh even that is stretching it, but wanted to give extreme example of low level damage causing a crit. A broken bottle probably won't severe an arm either or get anyones brains blown out but it can kill and cause pretty bad damage)
So if you think about it, whether or not a "cracked hip" needs a surgery kit or doctor's medical kit or anything is not relevant, what you as a referee say is needed to mend it goes. Common sense and "TV -medicine" goes a long way.
That being said if you want guidelines, if the wound is
lethal I'd usually set a requirement of surgical kit to HEAL it. If doctors kit is also used, I'd give bonuses. For STABILIZATION purposes I probably would require only doctors medical kit.
Then again first aid TO STABILIZE for punctured lung can be given okayish with plastic cling wrap and duct tape. Perhaps you could give bonuses to players who know some stuff like this (even if from movies) and can give colourful descriptions on how they "McGuyver" it?
So summary
To stabilize lethal wound: Doctors kit (drugs, clamps, better bandages etc.) Sometimes personal medical kit might be used instead, especially if the wound is described to consist mostly of bleeding or gash os slash etc.
To heal a critical wound: Surgery kit most of the time. Needed to fix things gone the wrong way. Sometimes doctors medical kit might be used too. Perhaps give bonus if both are? If you want to get more realistic use of alcohol to disinfect might give a bonus too and eat up players resources.
To do recovery (0 health): No requirements, personal medkit to give a bonus. Doctors kit to give more bonus.