In this sentence, Semantically 'his' and 'John' come to refer to the same person.
Hence, both "his" and "John" are co-indexed.
However,Principle C states that an R-expression like "John" needs to be free and not bound to an antecedent.
Well, either that or, more likely, an account that makes "John" bound is mistaken. It is pretty obvious that "John" in the example is not a bound variable.
There is parallelism here between "command" and "C-command". Backwards pronominalization within the same sentence is okay when antecedent does not command the pro-form and neither does the pro-form command the antecedent. E.g., "The man who first saw her (= Mary) took charge of the donkey Mary was riding." In your example backwards pronominalization in the same sentence is okay when the antecedent does not C-command the pro-form, and neither does the pro-form C-command the antecedent.
Backwards pronominalization is also sometimes okay when the antecedent does command or C-command the pro-form:
"The man who first saw her followed Mary closely."
"His mother always loved John best."