That may be a realistic interpretation if this were real life but I don't think it's what the author was going for. After all, a parent can feel responsible for their child going through such a thing even if it has nothing to do with genetics--the fact that Mashima didn't come to that conclusion before meeting the mother means he isn't considering that as a possibility (and in cases like this, the author is usually not noticeably more insightful than the character).