Some guy's tend to have too wide a hand spacing when doing front presses, which can put undo stress on the shoulder and even the elbow joint structure. A close in grip puts the pressing muscles more inline with the actual press it's self, with the anterior delts, triceps and upper pec's (yes the upper pec's are involved in overhead pressing, though a minor degree). Like having the thumbs pretty much lined up with the lateral head of the delts.
Stopping at chin level (momentary pause) can put more TUT on the front/lateral delts, which also puts more TUT on the shoulder joints. Dropping below chin level, with a closer to shoulder grip...never too wide, should not cause any superior tension anymore than stopping at chin level, to the shoulder joints themselves.
Actually overhead pressing can strengthen the tendons and ligament themselves. Some don't realize that when lifting you are not only building more muscle mass but also strengthening those tendons and ligaments around the joints. Which in return encourages more muscle strength. Another reason lockouts and static holds can become important training aids for serious lifters and BB'ers.
Example: I have done dead stop presses off a PR, on past occasions. Set the pins at about shoulder level. The next position of the pins is at eye level. The final pin setting is a little above the top of my head to a couple inches below lockout. Excellent method to not only increase muscle strength but also training the ligaments and tendons that can allow the lifting of more weight over time.
Good Luck.
