What's usually going on in a "hot" military operations area (in the US)?
Military pilot here.

I can certainly understand why there's confusion surrounding MOA's, having been a Private Pilot long before I flew for the military, and I'm glad you asked the question.

The second post you referenced is exactly right. It is extremely common (at least in our training areas) to have  dogfighting and other tactical training with airspeeds above 500 KCAS, and altitude changes of thousands of feet in seconds. No one uses a MOA for instrument approaches. This type of flying occurs multiple times per day, and it's extremely frustrating when civilian aircraft fly through the airspace without talking to ATC. We generally don't have a lot of time to work in the area, so we have to maximize the training we get. Stopping a fight/intercept/practice bomb run because a Cessna wanted to transit the airspace generally results in a reset of the entire scenario and wastes countless dollars and training opportunities. 

If there's an emergency we will, of course, understand and please do whatever keeps you safe. Short of that, please, please get flight following, and do not fly through a MOA.