Earlier quoted context omitted.
Indeed, this approach seems like a lawsuit waiting to happen. Push-ups are, at-best, a difficult exercise to get right (see http://thetoptwoinches.wordpress.com/2007/12/04/100/ ). Do them in bad form and you can injure yourself. Is the team leader going to be both an expert at management AND an expert at physical education? Does the company want the lawsuits if an employee is injured exercising at the direction of th…
That's not what "hostile work environment" means. Mandatory pushups are one of the dumbest ideas I've ever heard of, but I assume you are not going to be fired if you don't do them. When everyone starts doing pushups, go out for a quick run, or something.
Likely? No. Possible? Yes. Something to watch for but not something to stress unduly about.
[0] Remember, hostile work environment is not about any specific protected class (age, race, etc), but about general feelings of harassment and discomfort. http://en.wikipedia.org/wiki/Hostile_work_environment