When I was in BA, and I flew both Longhaul and shorthaul, MedLink was available, but was ronly really of any practical use in LH, using satcom, when you could actually speak to someone.
In SH, on the A320 aircraft, iirc, most did not even have hf radio, so to contact Medlink you had to use acars. It was just like trying to have a conversation via sms - ie absolutely pointless in an emergency. Indeed, I recall diverting in an emergency and being on the ground in 15 minutes in Europe with a very sick child. How did we decide to do that? By me as Captain and the Cabin Crew deciding that the situation warranted it - n outside or other on-board assistance. Were we right to do it - absolutely, the child survived after a lengthy stay in hospital.
Does this translate to this case, we don't know. Do BA SH still have the same facilities, or better, I don't know.
As others have said, it all comes down to the timeline and the quality of the information made available to the Captain from the cabin.