The key for me was talking to the right people. You really have to keep pushing and finding different ways to communicate with the PT's themselves. (emails, clinic phone numbers, face to face, etc.) I had more success talking with PT's and PTA's when compared to talking with the hospital reps. I agree with @SaraBoBara that you should try to target military hospitals. They seem to have more volunteers pass through. I would also try to avoid using the word "volunteer" and use words like "shadow". Don't be discouraged, I heard "we don't allow volunteers" as well.
However, getting on base seems to be the biggest impedance for civilians looking for military shadowing hours. I used my veteran ID to get on base for all of the military settings I was able to observe. A military PT could be your "escort" to get on base and around the clinic, but you have to find a PT that is willing to go the extra mile for you and it is never fun feeling like a burden as a volunteer. If you can not find a motivated PT to get you on base, try to look for military or VA clinics that are off base, or even a PT in the civilian setting that is reservist.
I hope this helps, and good luck!