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Depends on the depth of their bond. hell, it may even behave like Honedge (a fresh-caught Honedge played with in Amie/refresh will happily allow its trainer to play with its cloth tassel, but if the player bonds with the pokémon first, it gets angry when its trainer tries to touch it as it can't control its ability to drain life force and doesn't want to harm its trainer).
Either Ninetales would stop or prevent you from touching its tails, due to being unable to control its powers and unwilling to curse its trainer, or it can control its powers and eventually will allow its trainer to touch them, once their bond is sufficiently strong enough.
I'm more inclined to believe the latter as the whole franchise holds the bonds between trainers and their pokémon as being able to surmount anything, that should include a Ninetales cursing its trainer for brushing the knots out of its tails when grooming it.
