Would have to disagree on that one. If you do them close to failure every day without conditioning for it, you can definitely get overuse injuries.
But if you build up the work capacity before trying to do max or near max reps each set you'll be fine. About 4 or 5 guys I train with routinely do over 100 pull-ups every day and we're not some freaks, we're just a bunch of average bros.
When I started doing 100 reps a day, I could do about 20 reps in one set, but just did 10 sets of 10. Never had an elbow issue. In the past, when I only did pull-ups 2x a week working to or close to failure, that's when I had tendinitis.
Perhaps the program is the issue here, not the goal.