To me this sounds like a CSRF problem. There's no token or session associated with these calls, so a browser was able to inadvertently CSRF the calls. Changing this call to POST or PUT would still leave this API vulnerable.
It's not about access control, it's about the fact that browsers are free to make speculative GET requests whenever they like, and they actively do to pre-fetch pages. His GET end-point was pre-fetched by his browser, activating the door. This would still happen even if there was a token or session associated.
