Source: https://www.tatrabanka.sk/en/personal/cards/my-doctor/#MRI
I don't know if it fits here, but getting an earlier appointment because of what bank/CC you use feels... odd.
Isn't this just ragebait? Scrolling up on the page shows the explanation:
It looks like "My Doctor" is a third party service, and this bank is simply including a subscription to this third party service for the bank's card holders for this specific card. There are likely ways to subscribe to this "My Doctor" service completely unrelated to holding a specific bank's credit card.
Banks are always looking for value add services to entice customers to sign up for their bank card over competitors. I got a Visa card recently that has a card holder benefit of offering free cell phone data in foreign countries. What does cell phone data have to do with Visa? Nothing, but its something the bank is bundling in with being a cardholder.