I also find it hard to believe any Captain would deny a request from the CS to contact Medlink unless there are good operational reasons for not doing so. I have found Medlink very useful on several occasions and they have most certainly saved me from at least one diversion.
However, it would seem prudent to see if there are any medically qualified personnel on board who would be better able to communicate symptoms to Medlink. I certainly would insist on the crew exploring this avenue before contacting Medlink, it does not take more than a few seconds to establish if you have a willing qualified individual on board and it just seems to me to be a common sense first port of call. You then may have access to the Doctors kit and it could end up saving a life, which is after all the object of the exercise!
Having said all of the above the Captain is the line manager and if in his/her judgment it is not feasible to contact Medlink then that is the Captains call not the Cabin Supervisors. I would hope the Captain would communicate the reasons to the CS of course.
Prs777 the reason you would look out the window if asked by your Captain is because he is your boss for the day. You are required to obey all his/her lawful commands by law! That said airline operations are a team sport and we should be working together to resolve these sorts of problems. There may have been a good operational reason for Captain to deny such a request but as I have already said one would hope the Captain would have communicated his/her reasons to the CS.