Checking if a throw resulted in a capture server-side would be weird, I don't see why it couldn't be done on the client. It could be querying for the players inventory, to see if they have enough pokeballs? It'd still be better to just sync that once before the fight...
My best guess is, the conditions for a Pokemon running away involve something only the server knows. A weak example: maybe it considers other players in the area - pokemon might be more likely to run away if the area is too crowded? So every once in a while the client asks the server how many players are there nearby, or something.