He is not her cousin since you wouldn't call your cousin a distant relative but rather your cousin. So, He is probably her cousin's cousin or maybe her grandfather's sibling's grandson or someone even more distant. With that, there would be no problem with their child. Since the blood relation is almost non-existent. (づ ̄ ³ ̄)づ
These problems on offspring has a high possibility of happening between siblings. Small possibility between cousins. However, I never heard anything about possibilities between distant cousins. Well, blood relations between distant cousins are almost non-existent so there shouldn't be such problems. (づ ̄ ³ ̄)づ
However, it could be a passive genetic disease if the problems on offspring happen between a pair who are not suppose to make problems on offspring. Both parents might be carriers of passive genetic disease which made it possible for their child to have the genetic disease. ╮( ̄▽ ̄)╭
Incest is not my cup of tea. How distant are we talking here? (╯°Д °)╯╧╧