I don't know what the OP means when he says, "Umpire acknowledged hit by pitch." There is only one way for an umpire to acknowledge a hit by pitch, and that is by throwing his hands up and calling, "Time." Once time is called, he can adjudicate the variables and make awards based on whether the batter swung, whether the batter was struck in the strike zone, and whether the batter permitted the ball to hit him. But in all cases, when a batter is hit by a pitch, it is a dead ball.
Therefore, if the umpire acknowledged the hit by pitch and then ruled the ball live, as the OP reports, that is a self-contradictory call. The losing coach should have immediately challenged the ruling. If the coach permitted the umpire leave the field without being asked to explain, that's the coach's fault.
It's possible the ump spazzed on the call and the coach also spazzed to let the error go unchallenged. But it's also possible the OP did not understand fully what the umpire ruled. I can imagine scenarios, but I wasn't there and don't think the description gives me a clear idea of what happened.
Unlike some, I don't fault the fan for asking questions, as long as it's done politely. They don't post signs telling fans not to speak to umpires, so I don't expect fans to know the protocol, which is for the umpires to leave the field together and walk briskly away without acknowledging anyone or discussing anything until reaching the privacy of wherever the post-game conference is held. More than a few times I've had to ignore long-time friends when they tried to shake my hand after games--and then emailed them later to explain.
In my association, we are strictly adjured not to engage the fans at all, ever. Fans can say what they want and ask what they want within the bounds of decency, but we're not allowed to answer or acknowledge. So if you ever try to speak to me after a game, I'll regret it if I appear rude as I walk by you with my eyes in the boat. Please understand I'm following my association's rules. I can only hope a game's worth of courteous and professional conduct will outweigh the brief impression of arrogance.