But the question asked by the OP was is a bright line rule appropriate? that seems to me to invite discussion of what the rule should be .... as opposed to discussion of whether the rule should be followed.

Always interesting to see how others do things ... Where I've played it was either 3 folds or an 'action' (call or raise) with a reaction (fold or call) behind that was 'enough' for significant action. So this is either 3 or 2 players depending on their actions for 'the bar' in a ruling. Certainly makes things more complicated but that's what I was brought up with.

Does the rule mention 'full ring' game? If so, 3 people make up 33% of the table whereas in a 5-handed game 3 people make up 60% of the table. My point is NOT that we should teach floors and dealers how to calculate percentages, it's that 40-60% of the table acting should be considered significant and thus lesson the argument for a bright line ruling.

In this particular spot it's easy to blame the dealer for not taking the time to make sure of UTG's action before moving on AND not pulling in the cards quickly. It was Seat 5, get um out of there!!

It would be interesting to know if the dealer told the floor about UTG's actions and that he ruled a fold and thus moved action onto OP. GL

There are a lot of ways to move your cards around to stack chips without doing the above. Pushing your cards forward facedown and (presumably) releasing them is the literal definition of a physical fold. (It's also a complete failure to protect one's hand.) Moreover, the fact that both the dealer and next player(s) to act took it as a fold is significant in terms of how it must have looked. Whatever his intent, this was apparently a clear fold, and should be binding.
(OTOH, it would not be wrong or very unusual for the other players to agree to roll the action back and let UTG review his cards and act. But this would be a courtesy, not a required ruling.)
In regard to reducing the number of players who need to act to create significant action in a short-handed game, I do understand the logic, but I think this is a bad idea, because it's really a question of giving the original player enough time to have a fair chance to speak up, and this doesn't change with the number of players at the table.