I agree with you: he could not have gotten scars like that from a rock. Therefore, I think he probably did get these scars from the Black Rabbit. Also, he has scars immediately after getting out of the rocks, which is humanly (or rather, rabbitly) impossible. Even though it's a show that doesn't have much blood, he should not have scarred that fast. So, I think it logical that he got the scars from the Black Rabbit. I'm probably reading into it too much, but that is my opinion.