I haven't read all the responses yet but it's clear some additional context is needed.
This was Event #5 of a six-event league schedule. The vast majority of the players are regulars who've been in the league for a year+. The issue of collusion/chip-dumping is 100% a non-factor.
I try to run the game as close to what you'd find in a casino as I reasonably can. Game integrity is paramount.
I often employ dedicated dealers when I'm able to. In the absence of dedicated dealers, a player or two will almost always volunteer to serve as the dedicated player/dealer for the table while shuffling duties are passed around. At our table, Player A was the dedicated dealer that night.
This is why Player A, while UTG, was also the physical dealer in the hand.
To clarify:
Once the action was complete,
both Player A and Player C's hole cards were tabled face up consistent with casino/tournament procedure.
Upon learning that Player B also held 2 sixes ('allegedly' if you want to go there... but I know Player B wouldn't lie),
Player A then turned his cards over and mixed them in with the other mucked cards, making them irretrievable. His hole cards were exposed for not more than 2 or 3 seconds. The stub remained undisturbed.
So while we know he held two sixes, no one at the table (including Player A) could recall with 100% accuracy
which two sixes he held. And since Player B also mucked two sixes, all four of them were mixed in with the dead cards.
We can debate the 'why' part of his action... maybe it was frustration... maybe a momentary lapse in judgement where he failed to realize he wasn't drawing completely dead. I don't think it's productive though to speculate about his motives. Player A is a good friend and man of integrity. There was no ill intention here.
So I guess the real question is:
Is this a 'contested pot' or not? If not the correct decision is obvious.
And I supposed the player/dealer aspect of this whole thing makes this less of a 'what is the correct ruling' and more of a 'WWYD' type of scenario.
No one else voiced an opinion - nor did I state as much in the OP. I'm not sure why you're making assumptions.
To answer your question: In the moment, since I witnessed Player A's hole cards personally, I ordered the board be dealt in accordance with procedure. Had the board run out favorably for Player A's sixes - i.e. a straight - I'd have awarded the pot to Player A. If the board resulted in a chop, I'd have split the pot.
I don't know if that's correct - just how I would have handled it in the moment.
So you'd have called the clock on yourself even though you're not in the hand? I'll remember that for next time