I think that there was supposed to be errata to add an intervening "If" clause there, but it seems that somehow it was removed. See the "Rulings" from Gatherer:
10/4/2004 The Mogg Bombers do trigger on any creatures that enter the battlefield at the same time they do.
10/4/2004 If multiple creatures enters the battlefield as the result of a single spell or ability, then it will trigger multiple times, but due to the errata, only the first resolution will do 3 damage. The other triggers will do nothing.
10/4/2004 The "if you do" only happens if you successfully sacrifice this card. So it still has to be on the battlefield when the trigger resolves in order to deal damage.
You can find the errated version here:
http://web.archive.org/web/20091011044330/http://gatherer.wizards.com/Pages/Card/Details.aspx?name=Mogg+BombersI have no idea if this was done on purpose or by accident. But, until someone goes and fixes that, your combo absolutely works. Maybe someone was being cagey durring the M10 rule updates? All I can tell you is that at some point after July 11th 2010, the errata got dropped and the old wording (with the battlefield terminology) was restored.