Many companies use Medlink.
Takes the ball out of the Captains court. It is in some ways a form of insurance We call them with details of the pax medical condition, these details are passed onto a doctor/consultant, and hey presto, they tell you whether you need to divert.
if they get it wrong, it was their call, and as such the company/captain are not held accountable. This generally results in fewer unnecessary diversions, but what they also do is if you need to divert to somewhere with specialist equipment they can tell you where to go. They are also very good for gate screening, because although you may have a fit to fly certificate, they are on occasion, not worth the paper they are written on.
I have had one occasion where we could not contact medlink for whatever reason, but chose to divert anyway as the paddles were out.