When people say it's bad for the shoulders, it really sounds like a bullshit excuse to me, like they haven'y even tried it.
I don't know if it happens to everyone, but when I going for PRs, my first body part to complain is the lower back, not the shoulders. If someone told me "man, I wish I could but my lower back refuses to cooperate" it wouldn't roll my eyes at all, it's not an easy move,
OHP is in a certain way a "safe" exercise because the barbell will just stay there and refuse to go up, that's failure, nothing else. It's not like squat or bench in which your safety is at risk.
The Case Against Overhead Presses
There are lots of big dudes in my gym and with wide backs and nice physique. The squatting rack is usually free and I don't think I've ever seen any of them doing deadlifts.
Dunno why you're bickering over what kind of exercises someone does as long as they get good results. Considering all the injuries going on in this thread that almost even seems like a more reasonable route to take.