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If I have a rhino that's completely surrounded by enemy models, and my opponent attempts to assault with a monstrous creature, or any other unit for that matter, but can't get into base contact due to the intervening models, he can't assault with the monstrous creature or other unit, right?

Correct; if the second unit cannot make contact then it cannot assault.

The assault fails and the assaulting unit stays where it is.

But the unit that is in base contact with the rhino is not locked in combat, so on a subsequent turn, he could move and reposition the first unit, charge the rhino again, and leave room for the second unit to get into base contact to assault.