I'm going to have to say that things travel with the creature, for two reasons:
Firstly, because that means anything in the stomach of a summoned creature drops. Non-PC food, even. But I'd say air falls in the same category. Which means the monster can end up with lungs all the way open, but with nothing inside, and then air rushes in, killing the monster. This just doesn't make sense - there has to be a line in what is part of the creature and what isn't, and I'd say anything in the creature is part of it. Sure, feel free to disagree, but I say the creature contains anything inside itself.
And secondly, because donning your acid-resistance items and spells and hitching a ride to the lower planes in a fiend's belly is a plot hook too hilarious and unique to pass up.