And who decides that the criteria are met and is that decision also a dogmatic fact?
Well, if there's dispute whether or not the criterion has been met, then the criterion has NOT been met.
I believe that the principle cannot be Universal Acceptance alone, but must rather be:
LEGITIMATE ELECTION + Universal Acceptance.
So, in other words, if there's universal acceptance that the election being held is legitimate, then the results of that election make the man Pope. If five minutes later, the Cardinals inside the conclave tried to depose the man and haul out another one, that man would not be pope. Sound familiar? One Cardinal Siri scenario immediately leaps to mind.
Now, the counter argument is that the universal acceptance of a false pope compromises the infallibility of the Ecclesia Credens, but I would answer that the infallibility of the Ecclesia Credens is not compromised by material error.