The issue as OP sets it forth has nothing to do with status, but size of his bag. He had a factual dispute with the BA agent which the sizer is there to resolve. The bag either fits the sizer or it does not.
Presuming that the specific sizer in question meets the BA dimensions (let us presume that it is standard and does), there is simply no dispute.
The fact that the bag fits the OH or that there is space in the OH is not relevant to this immediate situation (although I can appreciate that BA, like most carriers, cuts off larger compliant cabin luggage when the OH bins are nearly full in order to avoid backup problems.
Holding the BP and phone seems silly. I can;t imagine that anyone would physically disobey a directive not to board or that, if that ocurred, BA does not have easy recourse.