JCat,
Yes, it makes sense. I guess. But on a 50A connection I would think you should easily be able to run 2 ACs, microwave, water heater, refrigerator, etc. without tripping the breaker. Perhaps that pedestal had a "weak" breaker. Or, perhaps the park had "low voltage" and the AC units were drawing more current than normal to compensate. Remember that a properly operating "50A" connection can supply 50 amp on EACH leg, for a total of up to 100 amps.
We've never had a problem in our rig and I would think that a third AC should be no problem, as long as the loads are properly balanced in your breaker panel.
That said, it certainly doesn't hurt to have the separate shore power cord, as it might be able to help in situations such as you encountered.
Good Luck,
~Rick