Given how snide and ignorant the parent was being, I actually think their response was entirely warranted. You better not be insecure about your own credentials if you've got the balls to question someone else's authority on engineering. Turnabout is fair play.
Oh please. They didn't even claim to be a member of AIE, they just said their university/degree was "accredited" by them. You know: the absolute bare minimum requirement to even call it a degree? You're really impressed by that? Would you be impressed if someone told you they were a member of IEEE? It's just all the same bullshit.