It would make sense that if the Kyurem and Reshiram have their natures set during their catching. Remember, trainer's Pokemon are randomized, while Elite Trainers have good natures and IVs. Kyurem-W was previously own by Ghetsis, so it must have had a good nature. When I caught my Kyurem, it was a Brave Nature.
Recall that N's Pokemon all have 30 IVs in each stat. Meaning it should have an HP Fighting. When I took my Reshiram to the Hidden Power checker in PWT, it was an HP Grass....
Also, my Reshiram had a Adamant Nature when I first caught it.
So it is safe to assume that they are set when you first catch it.