It's not because no one else in the Senju clan did not use Wood release that it wasn't genetically transferable. It's quite possible that it's just so advanced that other weren't able to do it.
F.e. There are people in the Uchiha clan that go on their entire life without unlocking the Sharingan, that doesn't mean that they don't have it, just that they are unable to unlock it.
I think wood is a bit tricky on the matter of KG's if you look at it this way.
Same thing for Dust release, it's a Bloodline Expansion, and it requires 3 elements. Still, it can be passed down to people who aren't genetically connected...
F.e. There are people in the Uchiha clan that go on their entire life without unlocking the Sharingan, that doesn't mean that they don't have it, just that they are unable to unlock it.
I think wood is a bit tricky on the matter of KG's if you look at it this way.
Same thing for Dust release, it's a Bloodline Expansion, and it requires 3 elements. Still, it can be passed down to people who aren't genetically connected...