I will 100% grant you that the rules do not have the granularity some may want and do not discuss "verge" of death type situations in as much detail as one may like. I don't believe this is some big undersight as much can be role played. Stats that are total obliterated into double digit negatives can be brain splatted when applicable. Stats that are barely into death can be role played as verge of death and didn't make it when applicable. Stats where one is just barely alive and receives medical care can be role played as verge of death and brought back by the miracles of modern medicine when applicable.
For some, perhaps many? It is not an issue as their games are more about diplomacy, trade or other things.
So let's move away from the extreme cases and towards something a little more common in Traveller.
What if the character was shot twice by a shotgun and reduced to 000777?
There is no Classic Traveller hit location in the core rules, but I think that it is safe to assume that he was probably not shot twice in the thumb and bled out. Statistically, a shot to the center of mass is more likely than a head shot.
So for the sake of argument, let's call it a shot to the chest and arm and a second shot to the belly and leg (this is a shotgun after all).
Who in Traveller doesn't wear some form of cloth armor or other body armor? (rhetorical question) Especially if they are the type to get into combat. Doesn't typically cover the head though. My point is that someone who lives in a Traveller society would know the medical and combat norms and if they want to kill or even stop someone would likely be aiming at the head, not the thumb, not the chest.
Despite that, I'd say stipulating 000777 occurs from non head shots is biased toward an argument for 000777 stats not really being dead or killed or for death to be recoverable.
For someone that does not believe such, 000777 could reflect a hit to the head which cause unrecoverable damage and 200777 would possibly be "a shot to the chest and arm and a second shot to the belly and leg".
Who hasn't been on a low tech world and thrown a comrade into a Cryoberth until they could be taken to a high tech world with proper medical facilities? (rhetorical question) My point is that I believe the rules are written around a higher future TL where a gunshot to the heart is recoverable and only represents 000XXX when you role play it that way, not because the rules say so.
Now, both the Known Space autodoc and the nannybags are (presumably) above TL15, but MgT is a generic rules set, right? So given a sufficiently advanced TL (17 or 19 or whatever is the appropriate level), the MgT rules ought to accomodate this sort of thing.
No reason a rule can not have exceptions. There are examples in the core rules. For example there are rules on dodging and it's effect on initiative but an item in the equipment list, Combat drug, allows a dodge with no effect.
I believe there is a MgT publication that covers putting a brain into a cybernetic body?
So the rules allow for all sorts of possibilities even if they don't spell them out.
Details of a setting and deciding the capabilities of technology not fully described in the game are the norm. I don't think it would be against the rules to clarify for ones play group what a field med kit, medical lab, and fully equipped hospital can do at different tech levels. For example, the rules provide only the briefest descriptions of the difference between a TL8 and TL14 medkit and there are also TL10 and TL 12 versions. What could one do with a TL16 medkit? As I've mentioned before, I believe it is possible for one to interpret the rules to allow surgery to be performed on someone who's stats are 000XXX or below. You could say this is only possible at a certain TL or higher hospital and these are the type of facilities that could grow organs and such. Same with first aid and medkits. You could start writing volume one for your Traveller medical library and detail all kinds of possible combinations of trauma, poison, diseases and other medical conditions and the ability of different first aid, medkit, medlab, trauma centers, and hospitals to handle such.
Or you could wing it and roleplay based on the situation that occurs in the game.
For a bit of realism, how about in real life more young fit military folk die from causes other than combat. (2012 statistics) Or the odds of dying in a fall are 1 in 184.
Imagine your character taking a shower before bed, slipping in the fresher and hitting their head, unconscious, bleeding out, and nobody going to check on them until the following morning.
Dead?