I encourage my kids to excuse themselves when they pass gas. (Obviously the best-case scenario is that they are able to release it in the bathroom instead, but things happen.) I have a few goals with this: acknowledging that there's going to be a brief bad smell in the room, accepting responsibility for it, and begging pardon for inflicting it on the other people in the room.
I feel that encouraging silence instead of acknowledgment completely misses the second and third goals. There's very little chance that the smell will not be noticed if there are other people in the room, and especially if there are other kids around this can lead to a great deal of blaming, arguing, and bad feeling. This can be avoided by a brief apology before the smell really spreads.
There are different kinds of acknowledgment, however. I would consider a simple "excuse me" to be polite. If they proclaim "EXCUSE ME, I HAVE JUST FARTED AND IT WILL PROBABLY STINK," or "I farted! [endless laughter]"... that isn't helpful.
My goal is to get them to understand that this is something that can happen to anybody, and it shouldn't be a gigantic source of embarrassment or shame, but it should also be dealt with rapidly and briefly so everybody can just get over it and move on with their lives. This isn't particularly easy, because kids tend to find bodily functions both highly amusing and highly embarrassing, but we're working on it.