Over the years, the study has been rebutted with solid, scientific justifications. In fact, science has proven that the compressive forces of the knee is at its maximum when the squat is AT PARALLEL. The compressive forces, contrary to your belief, reduce at the bottom of a squat (ass to grass).
Advocating the full ROM squat, another point worth noting is that the knee health actually gets better (weight training strengthens not only muscles, but also bones, ligaments and tendons) with performing perfectly executed deep squats.
Then, why so many cases of injuries among trainees? Injuries are often a consequence of poorly designed programs and/or improper form. There is zero scientific explanation to the belief that correlates depth with poor joint health. Squatting deep is hundred percent safe, unless done improperly. So can be said for drinking water.
Case #2 -“BRO, THE LOAD IS SO HUGE! OFCOURSE, THE RANGE WILL SUFFER WITH THAT!”
Okay Bro, I love the fact that you want to do a heavy rep. Except, it SHOULD LOOK BE ONE REP, NOT A QUARTER. If you think you’re getting beastly strong and giving a supremely high stimuli to the muscle when you’re only partially squatting 200kgs (in that case, even the guys who Leg (quarter)-Press 700kgs), I have bad news.
A word on Motor Unit Recruitment: This term basically indicates how many muscle fibres is your body recruiting for a particular task (keeping things basic). Having said that, it doesn’t take a genius to figure out this equation: More motor unit recruitment = more muscle fibres involved = more muscle hypertrophy (muscle growth).
Now consider another (very simple) equation: More Range of Motion = More Motor Unit Recruitment (This is scientifically backed and proven). Take a page out of your childhood algebra and mix the two equations, which leads to this:
FULL R.O.M. = MORE MUSCLE HYPERTROPHY.
Getting back to your Bro’s heavy quarter squat PR, the bad news to be broken to him is that all he did was build his ego, not his strength/muscle.
Consider a parallel to this case. On day 1, A 100 meter sprinter runs at the speed of 23km/hour. On day 2, he runs at the speed of 24km/hour but fatigues and stops at the 75th meter. Did he break his running PR? Of course, not. The entire 100 meter track is Full ROM for us lifters. So, every time your Bro expects a pat on his back for his quarter-squat PR, smile and tell him that he only ran 75 meters. (Also give him the explanation if you don’t want to sound stupid.)
Bottom Line: Do a heavy rep. Not a quarter/half of it.
Case #3 - “BUT TOUCHING THE CHEST IN A BENCH PRESS LEADS TO SHOULDER INJURIES!”
When done correctly? No way. Going full ROM on a bench press in an improper form may lead to an injured shoulder. Going half ROM on a bench press in an improper form may also lead to an injured shoulder or any other muscle. Note the keyword: improper form.
The important take-away is that your form and technique has to be taken care of first. Get your form checked under the supervision of a certified trainer and avoid drowning into the typical flood of misinformation widely prevalent in the gyms.
If done in good form, there is no reason on earth to not get the benefit of more muscle fibre recruitment with a full ROM bench press.