PFan - I think there is a difference between a tight hammy and a sore elbow in a baseball player. One is a cause for immediate concern of long term (life altering) injury and the other will pass. So pain vs. injury is a real debate but a different and more serious problem is care for those injuries and who is giving it.
Honestly if you address the care issue I think the pain vs. injury usually sorts itself out pretty easily most of the time.
Players want to play almost all the time. It is the job of parents (in HS & below) care giver, coach in that order to determine playing time once an injury occurs. I know this will be controversial but I believe coaches should have very limited influence on this - they are not qualified unless they are medically trained and I never saw one that was. The care giver should be at the discretion of the parents and whose opinion is guiding the decision should be the families and no one else's.
Once a player reaches college things change. But until then it is the legal imperative and morally correct process for the parents to make decisions of this nature.
As for coach - if he feels like he's got a player dogging it in practice faking injuries - the bench is a nice place to put him after he refers him to his parents for medical care. See that whole string about coach puts hands on player and got arrested. This is an extension of that. Don't push things - be cautious - it is part of the job now.