Two players are heads up (cash game).
The turn card is dealt and Player A makes a bet. While Player B is considering what to do, Player A announces to B that he's going all in once the river card is dealt. He is fully aware that B has not acted yet on the turn card bet before him.
Q: If B calls the turn bet, is A bound to go all in on the river?
Nope. It's not his turn to bet so his verbal is not binding.
If B calls then A can announce he is shoving blind on the River though and that is binding.
I agree with your answer (that its not binding) but not you're reasoning.
I don't think it matters that it is not his turn to act. You can act out of turn and as long as the action has not changed to you, your verbal declaration binds you.
I don't think A is bound to shove in a subsequent betting round, even if B flat calls. It's a new betting round, not acting out of turn on the same betting round without the action to Player A changing.
It was probably more a matter of Player A having bet-remorse (wishing he would have bet more) than an angle shoot, but I agree that a warning is probably in order.