[UberRoo]

If you tried to tow it in park, you'd know it right quick. Also, I'm pretty certain that the parking pawl (which locks things up in park) would not screw up any planetary gear set.

A transmission fluid swap is a low risk affair. An actual flush on the other hand, is a somewhat risky venture. If they flush things with any pressure, or worse, if they back-flush things, any debris that may have been harmlessly lying in some safe little nook or cranny suddenly gets swooshed away by the fluid. Where it gets swooshed to isn't always known, but it's far from unheard of for those little nasties to get stuck somewhere bad instead of making their way out the drain hole. Usually nothing happens, but I found a few transmission shops that wouldn't do any flush for this very reason. They said it's usually harmless, but every so often...

The "towed in park" story makes me suspicious. Who's that stupid? (Nevermind, I'm sure someone is.) My point is that it's a pretty unlikely explanation that doesn't make sense anyway. I wonder, are the people who came up with that idea the same people who did the flush?...

It may not be related, but there's a strong case based on the circumstantial evidence.