I did these exercises during all my stints as a player and so has my son and some other kids I've helped. We have never had an arm injury of any kind due to these exercises.
The only time I ever had arm soreness was for a brief period of time when I listened to my coach and iced after pitching. I quickly ditched the ice and never looked back.
My son has never missed a start due to arm soreness and has never left a game due to fatigue at any pitch total less than 120.
If a shoulder gets injured, it's not due to the pullups and chinups, I can assure you that.