Personally, if my job responsibilities included anything that is synonymous with managing or supervising, then I would say something. If not, I would mind my business.
Perhaps that individual might get lucky and the manager, assistant manager, supervisor or supervisor might see it and offer constructive criticism.
It might be better received from someone who has that responsibility as opposed to someone who has the same responsibilities as you do have.
I tend to lean toward handling situations in such a way that promote collaboration. We have enough drama between personal trainers going on already.