I agreee with Jules...when my father-in-law ran marathons, he had to put band-aids over his nipples to keep his shirt from rubbing the skin off the nipples.
Bingo! You figured it out!
26.2 Miles of running with fabric rubbing up against a man's nipples will indeed rub the nipples raw and cause the bleeding. I am a triathlete,endurance cyclist (100 plus mile events) and marathoner. Band Aides over the nipples prevent the rubbing or chaffing. I never leave home without my band aides.