You do see the problem, there?
Sure, wasn't clear enough. It is not about "bloodline" as in "mix as little with outsiders as possible" like some sects right now, it is a proof of belongness to the line of rulers. For example, mother of the pharaoe could have been a step-sister of his father, but for as long as she was included in the family in an obvious and clear way, it was accepted.
Basically, it is a test of "fatherhood" older that civilisation - you can't prove who the father is, but you can prove who is the mother, and she needs to be a part of the ruling family. Which, according to the multiple scientists, basically means that egyptian pharaoes were transferring the throne via female line all along, and there was very little of actual incest happening. It was more of a ceremonial marriage with pharao accepting his sisters children as his.
Greek pharaos, who on paper were inbred to the point of becoming unfertile mutants, showed very little signs of actual inbreeding. Cleopatra came out of that line, that on paper looks like a circle.