He doesn't have to prove that he didn't send them ... that's the prosecution's burden. (In the U.S. ... I know nothing about Canadian law.) But a competent lawyer could figure out how to prove it: get ahold of the IP address from which the messages were sent. Oh look, it was in California! (The IP address they had was from the email address with which Klayme had registered his Kik account with the mistranscribed name.)

Also a competent lawyer would have done a scrupulous audit of the chain of reasoning that led to his client, which would have revealed the username mixup.