As someone who competes in Judo, and as such needs as strong a grip and upper back/shoulders as possible, I have experienced this.
It's easy to overtrain pullups/chipups/rows and end up with tennis or golfers elbow, which is not fun, and takes a long time to heal, being a tendon overuse injury.
If it progresses to tendonitis, you're in for a lifetime of problems that are very debilitating. Think not being able to grab a dinner plate off a high shelf.
Don't treat pullups as something you can just grind. If you grease the groove, only do a quarter to a half to what you can comfortably do, and give yourself a maximum number of sets that you will do during the day.
Progress slowly over many months, with proper form and slow reps and no kipping. Don't do anything silly like add "a rep a day", or try to "drain the tank" every time you hit the exercise.
Just trying to save someone else the pain. It's surprisingly to override discomfort with willpower and actively destroy your own body
And in my experience, doing hundreds of pushups daily eliminated my chronic wrist pains caused by injuries in my youth (they've both been broken), and has never caused any lasting harm.
Considering we're talking about people who aren't doing any exercise at all for "lack of time", it's somewhat absurd to be muddying the waters talking about the opposite end of the spectrum; overtraining.
The point is to just get off your ass and do some trivial calisthenics every day before you bathe. In the early stages you're only going to be able to do a handful, maybe not even one pull-up without a chair to assist you, you're not going to "overtrain" doing as many as you possibly can in this condition: we're talking about doing very little. It's emphasized because the amount you can do is proportional to how much time it requires, it's practically zero.
In fact, the probable major result is a change in diet because of the brutal feedback attempting to lift your own weight repeatedly every morning can have.
I don't think for most people it's easy to overtrain, but it's certainly possible. Greasing the groove as you describe is much more typically recommended than "as many as possible". Myself, I actually started with a hanging regimen before beginning to work on pullup variations. I agree with most of what you say.
