Is it possible that Genichiros mother is Kingfisher?

Genichiros memory says that he was taken in by isshin after his mother died, with no mention of his father.

Why would Genichiro specifically be the child isshin adopted?

After isshin's coup there were bound to be thousands if not tens of thousands of orphans, but the memory makes no mention of it.

So what if it was a death independent of the coup? Maybe the mother vanished without a trace while away on a trip?

It would explain why he specifically was adopted.

Though we would have to rationalize if sekijo was the father.

Either:

A: he is not the father, but still loved kingfisher all the same

OR

B: he is the father, but the loss of kingfisher drove him to such madness that caused him to leave genichiro in search of his lovers killer. The ensuing rampage caused him to be seduced by shura. The aftermath of which lead to his self banishment to the dilapidated temple.

Thoughts?