I want to thank everyone for the input. From what I can gather, I was correct that constraining was the only way to flip parts around in precise increments. For the record, I wasn't talking about parts imported from MD, I was talking about any parts at all.
I'm in the process of learning IV, having worked with MD for a couple years, now. I try to keep an open mind about things, and sometimes my problems are from using the wrong approach. I've been convinced that IV was nearly unusable for certain tasks, only to find that it's easy to use with the right approach. So I understand the reasoning behind the "forget that MDT stuff" message.
On the other hand, I've found instances where a basic element of functionality (like, say measuring distances between features) is simply a lot easier to do in MD, and IV could really stand to take a lesson. I think this issue is one of those situations.
Yesterday, I was placing four bars into an assembly. The bars were to mount to a baseplate on four sides of a device, to sort of "fence in" it's location. I created one bar, and placed four instances of it in the assembly. Naturally, they're all at the same orientation. I need to spin two of them 90 degrees. I constrained each one to the baseplate surface, then did a eyeball-close-to-90 rotate on one of them. Then I mated faces on a second bar, with an 8" offset to make the second bar parallel to the one I rotated. *Poof* It disappeared. I zoomed all, and the constrained bar was a couple thousand inches off to one side of the assembly. Is this easier than using the power manipulator in MD? Not even close.