A border summit having two (or more) references is an undesirable necessity. I am sure you can appreciate the diplomacy and sensitivity required by SOTA MT when working with overseas associations. If two neighbouring associations that are different ‘foreign’ countries with different governments/administrations both want to include a border summit in their ARMs, then it is not the place of SOTA MT to tell them otherwise.
In the case of the UK associations, a single list (The Relatives Hills / Marilyns) covers all states, so there is no duplication. In Spain, where there are also multiple associations within the one (political) country, the AMs have worked well together to ensure that border summits are listed once only. The same applies within Germany (DL and DM).
Black Mountain was originally listed in the RHB lists as in England, so it originally had an English reference. That group now categorises that summit in Wales, hence the G reference was discontinued and replaced with a GW reference.
For a border summit to have two references, the summit must be right on the border. A mountain with its summit clearly inside one country, but with the activation zone extending into the other cannot be claimed by the latter. So the example you quote may be worthy of further examination, but the difference in summit heights may be no more than a difference in government-held data, rather than different ‘summit’ positions.
Anyway, Black Mountain is an easy walk. It hardly merits 6 points, let alone 12