Due to the phenomenal costs involved in medical diversion this is really only done as a last resort. Most of the major airlines have access to MedLInk which is a telemedicine system where a doctor will make a MEDICAL recommendation to divert in specific circumstances ( ie cardiac chest pain, stroke etc) although legally the Captain has the final decision about diverting the aircraft they will be guided by rge MedLink physician's recommendation. As the passenger is not medically 'fit to fly' at this stage the airline are within their rights to offload this person ASAP. I guess the passenger could try and insist on a ticket to continur their journey however this would probably be given AFTER payment of all the fees for the diversion which would be tens of thousands of pounds!
Better to have good quality travel insuramce and declare any pre existing medical conditions to the insuresr at point of sale I would have thought!
Incidentally airlines will not divert if there is a death on board