I don't see it so much as an inconsistency. I see it more as an omission.
You recall in Empire Strikes Back wherein Luke declares to Obi Wan, 'you told me Vader killed my father', and then Obi Wan goes on to say that in a manner of speaking, Vader did kill Anakin. It would seem Obi Wan has a way of bending the truth to fit his agenda.
In Episode IV, Obi Wan may have told Luke that Anakin wanted to give Luke his lightsaber because it fit an agenda to move Luke along the path to becoming a Jedi. Also, since Obi Wan thought of Anakin as a brother, he may have thought of Luke as his nephew or son.
Hello! Obi-Wan was there at the birth, he should have known this.
Maybe that is what
is going on in Bill's head --
thinks he's a Jedi . . .