If he is scrupulous about washing his back after sweating and you really think it is not related to lack of cleanliness, then it is probably acne. My dermatologist told me that she has SO many 29-35 years olds coming to see her about adult acne - its very common.

He should go and see a dermatologist. If he refuses to take mediation (though thats the best way to get rid of it) he could use Renova or maybe get regular glycolic peels. Both of those should help - though if it IS a bacterial infection nothing but pills will work.