Aircraft in contact with Tower and operating in the vicinity of an ATZ are receiving an ATC service and are expected to comply with ATC instructions - even if they're in Class G.
Many people would disagree with the above (Class G is Class G regardless of who you are talking to) even if it seems perfectly reasonable to me that one should follow ATC instructions since they are usually given for a good reason.
And here is a large part of the grey area that needs to be clarified.