Active duty personnel aren't allowed to take on a second job, side hustle, etc. without written permission, and I understand that that permission is relatively uncommon. That doesn't completely answer your question (maybe generals get that permission more often), but it may point directionally.

The other thing that can confuse this issue is that Generals and Admirals generally (sorry) keep their titles after retirement. So if you have "Gen. James McClinton" on your board, that doesn't speak to whether or not they're active.

From looking around, it looks like board recruitment efforts toward Admirals and Generals are targeted at those who are retired or nearing retirement: http://blogs.reuters.com/financial-regulatory-forum/2012/01/...