Taking a step back from the hand specifics, I was looking at SSH and it pretty much religiously says push the pot any time it's +EV to do so. Given the hero has 12 outs, pushing the flop is definiately +EV.

The only reason to give up the flop +EV is if you can get an even better +EV on the turn. SSH drills this in with examples of waiting until the turn, but in his cases the reason you wait isn't to make your hand, but to see if the turn is a blank and check/raise a made hand.

Examples are waiting until the turn in a big pot and top pair, but a flush draw on the board. Wait until the turn to push if it's a blank becaus your equity is so much better.

Our hero is in the reverse situation, most of the cards cripple the hero's equity because most don't make his hand. In this case the hero needs to push at the flop because that's where his equity advantage is. Yes, it's true if the hero makes the turn cards his equity goes way up, but not enough to sacrifice his equity on the flop.

If UTG was going to bet 100% of the time and the SB would always call, AND a river 4-flush won't give the pot way, then it becomes pretty close. Those are big assumptions though and whatever portion of the time those don't hold up severely diminishes the equity of waiting until the turn to check/raise.