I don't think PAs do, the general public does though. Same thing with nurses, but they are hit or miss. Most I've encountered say nursing school and are proud of it. I've met several, mostly younger ones, that say med school though. Example:
I was talking to one of my neighbors while I was walking my dog and when I told her I was in med school, she said, 'oh, I remember those days, it sucked but it really wasn't as bad as everyone told me it would be.' We talked for a while and she said she worked in the ER and sounded pretty legit until she said something along the lines of 'the physician said...' and I got confused. I asked her what she meant and she said she was a nurse. I asked her if she went to med school and quit or something and she said, 'well, I went to med school to be a nurse'. When I asked if she meant nursing school she got really offended and defensive. She said, 'you're just a first year, I have more knowledge in my pinky than you'll have in 4 years!!' After that I just said 'uhhhh, okay' and walked away. Haven't talked to her since, haha.