Possibly worth mentioning that since this topic was started, the permissions model changed somewhat, and there are now Observers (who cannot make updates, and which used to be called Guests 
) and Guests (who can make updates for the entities to which they are assigned).
Guests can press buttons.
The use cases mentioned in the original post are now possible for Guests.
However, it is not possible for anyone to press a button for an entity that is otherwise read-only (and likely will not be for some time).