I have the opposite of hyper-mobility. I used to play a lot of sports and do martial arts and stretching is a huge part of warm ups. My flexibility never would increase and I believe POIS has something to do with that.
Yes POIS prevents me from getting flexible. Stretching before exercises would make me prone to injuries. I had a few events were POIS made me stiff to the point where I had the idea I was pulling a muscle when using the affected muscle groups. Things I'm thinking about what POIS does:
1) Changing blood supply to muscles.
2) Affecting muscle tone (this one is quite clear to me, I think this one gives me problems in maintaining posture during POIS)
3) Releasing enzymes which degrades connective tissue (MMPs)
4) Inflammation (3 and 4 could be the same thing)