Fender has never used a brass nut on his bass guitars (not in those years anyway and not on common P basses). So it's certainly been added later.
This suggests to me even a refret job done on the fretboard, otherwise it wouldn't make sense only to change the nut.
In fact, looking at the picture, the layer of rosewood is very thin, so the keyboard could have been leveled somewhere in time (common fact during a refret job). Even more so if you say that the frets are still like new.
I sold an identical P Bass (same year, same colour, same features, same amount of money) just a couple of months ago. She also had a non original brass nut, and a really thin layer of rosewood (that I think was leveled several times). My 2 cents.
Anyway, it's an amazing instrument, in a very good state at a fair price. Good luck with the sale.