I heard about MRSA while watching an ESPN story about professional atheletes that had contracted it in either workout or training facilities. I couldn't find a link to that story (I believe it aired on Outside The Lines) but here's a link to a Mens Journal story about the topic:
Without further research I can see how someone could mistake it for being an issue primarily of athletes and workout areas. However, MRSA is more of an issue in hospitals and the infection rate is extremely low.
The benefits of working out far outweight the potential risk of MRSA contraction.