Rather than "answering to none", the GM has to be able to establish legitimacy with authority, but in a way that doesn't alienate. You've got some heavy, strong language in the beginning, there.
I know that this particular issue of authority has a number of valid theories and leadership structures related to it. Establishing legitimacy of authority I believe is also a very important component of running a successful RP. However I must also say that the very word "authority" implies that the GM possess a level of command innate to the position. The way I see it, a player in joining an RP has given the GM a level of command over the structure of activity within the RP that the player will undergo. As a player, I believe one can't just enter an RP and do whatever they will against the wishes of the GM just because they haven't "earned" that player's respect/fealty. A player has made a sacrifice in agency in order to be a part of a world created by the GM and other players. A player in the end does have authority in that they at any time can choose to leave should things not be to their liking. Like you said VV, the GM doesn't want to alienate the players because if that were the case, the players would leave.
When I say "answer to none", that means that in my mind the final decision making lies solely upon the GM. Sure, players can make suggestions and protests in order to influence the GM's decision yet ultimately the last word is not theirs to have. Again a player at any point can choose to leave and a good GM will always be open to the opinions of the players as it is the GM's job to steer the RP in such a way as to satisfy the players. This does mean though that they can't let others
dominate their decisions, which is why I say "answer to none".
If the GM is not there to confirm the Co-GM's existence, there is no reason to believe them when they come out saying they've inherited the RP.
The existence of the co-GM is made public before the RP even begins, at least, that's the case in my experience. If there is no public announcement then yes, you're absolutely right, there is no reason to believe them.
Ideally, there should be multiple GMs. Not co-GMs, as that little co- right there is a useless limitation of the authority of someone who is /supposed/ to be helping a GM do their job and thus deserves the respect and title that comes with that work.
To me there's a functional difference between the two which is why they are differentiated as such. A GM creates the RP, it's backdrop and has an idea in mind as to the direction it will take. They steer the RP as necessary, make sure it doesn't get too far off track and handles grievances that may arise. A co-GM by comparison is a roleplayer who has access to privileged information and will also assist the GM in fostering greater cohesion between players. When the GM must take a leave of absence, the co-GM takes over the controls until the GM returns. Sure, a GM can do this as well but in my mind a GM must also actively manipulate the macro-structure of the RP. Two people doing this at the same time I find redundant unless the the scope of the RP is so vast that such a structure becomes necessary. I also find that it is no measure of disrespect to be called a co-GM for doing a co-GM's job. However if someone acting as a co-GM wishes to be called a GM, I don't see a problem with that either. That's on a case by case basis I feel though.
Ultimately, the "RPers vote in a new GM" concept is probably the best way to go about things should no GM remain left.
I feel this works as well when the RP isn't too ungainly in its numbers. However as the number of players goes up, so does the failure rate of this method of establishing new authorities (an eerie analog to state democracies). The structure of "inheritance" was established to bypass this problem and although this kind of unitary or oligarchical system may provoke some sour reactions, I feel its better that the RP continues to function despite maybe losing a few players. Now obviously if there is a massive protest to the proposed inheritance then things would have to be reconsidered.