Not a horse person, but I did look this up once. My understanding is basically what you were assuming.

There’s no way to tell the horse to not walk on the foot and the options they have to keep a horse off the leg can only be used for a limited time without causing death anyway. (You can’t put a horse in a suspension sling long enough to heal the leg as it supposedly does bad things to their organs)

So it’s feasible a centaur could recover as they’re smart enough to take things easy without needing to be physically restrained the whole time.