I'm not a physician, but I think that it really depends on the situation. An incorrectly performed reduction can have devastating consequences, but so can leaving a shoulder dislocated for an extended period of time. I think that in the example of a pro or college football game, there will usually be someone on-site who's qualified to fix the problem. If you dislocate your shoulder during a recreational game and your friend offers to fix it for you, it's probably best to visit the ER and have a doctor do it instead.
In certain cases - such as an injury that occurs in the backcountry hours away from any medical help - people have even performed their own reductions. Ouch!