I saw the film in 1989 or 1990, and numerous times since : it hadn't been changed. They just cleaned a little bit the picture, that's all. The only animation part is the little bear's dream. The rest is 100% real, even the cougar scene or when Bart is yelling on Tcheky Karyo (actually, he was not acting, he was really afraid of the bear, who was too close)
But Annaud said he couldn't do that again now, because he wouldn't be allowed to (by law) : is't far too dangerous. That's why he sometimes used CGI in Two Brothers.
I highly doubt the actor is in a same shot with a bear. It's just nuts, nobody is going to agree to do this. I assume it's one of the trainers who posed for stunt double.