According to medieval law, Batsars can't inherit.
According to medieval law
I should be very cautious about making general statements about a large region over a long period of time. It is not quite a full answer to your question, and more can certainly be said about how That Norman Git inherited his position. For the meantime, u/AlamutJones has a post re how William pressed his claims despite his illegitimacy.
As always, if anyone else would like to make a fuller answer to this question, please don't let this post stop you!