A pulled groin muscle is not that rare, though it isn't that common either. I have heard of several guys getting this in high school. In the cases I am aware of, the pain from the pulled muscle doesn't happen right away. And the cases I know of, the player went to a doctor. The coach did not try to "fix" it.
I don't know for sure, but I don't think it is a requirement to be completely nude to wrap the leg nor is it usually done standing up.
I can buy the three boys getting hurt that way in the same game better than I can believe the rest of the story.
Think for a moment. What coach in his right mind is going to, in a boys dressing room with guys everywhere, have three boys stand totally in the nude and have his head, as in his eyes and mouth, inches from high school boys' dicks? And while the coach is wrapping them, apparently at the same time, (this I gotta see to believe) all three display a semi hard on.
If you believe this story, I've got some rich farmland to sell right in the middle of the Sahara dessert. Ten percent off just for you.