Perhaps you didn't intend or expect it to be co-opted by a Burger King commercial, but "unauthorized use" (in the legal sense) might be a bit of a stretch.
> it seems that by intentionally [making available a server on the Internet] a device explicitly designed to respond upon [receiving the request] "[GET <URL>]" one could argue that you have authorized it to do exactly that.
FWIW, I'm not convinced that should constitute unauthorised access. I do think the Burger King case is slightly different though - no "OK, Google" commands would be likely expected from a remote third-party, whereas third-parties are authorised to make _some_ GET requests. If anything, I'd say that makes it more likely to be considered an unauthorised use.
Aaron Swartz certainly didn't break into anything. He just used a system he had authentication to in an unauthorized manner.