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Allowing methods isn't as simple as just allowing/disallowing them because
different methods do different things.

* HEAD: should be allowed everywhere GET is allowed.
* OPTIONS:
  * When a CORS request is made, this will be handled by the CORS library.
  * Otherewise, we need to return the allowed methods.
* POST: always allowed.
* Everything else: always denied.

Changing HandledMethods to a simple AllowGet makes it easier to "do the right
thing".