I have a simliar story. We sailed on Magellan Christmas/New Year 2018/9. It was two cruises, back to back. The Panama Canal trip. Many folk on the ships were sick with colds/flu etc. I caught it and decided to visit the medical centre. I was not told how much it would cost but I went for 4 days am and pm and had antibiotics IV plus oxygen. I expected a couple of hundred pounds. We live abroad and are used to private medical bills.
On the last night of the first cruise a bill appeared under our door around midnight for just under £3,500. I thought, OK, I will visit Reception in the morning as it must be wrong. I went at 9am....too late, they had taken the monies from my card at 3.30am !! As you say, you have to give your card details to reception on embarkation.
As we were staying on the ship for the next cruise, I decided to try to talk to personal and make a formal complaint. My insurance company, BUPA International were proving very difficult to make contact with. The Medical Centre said they had never heard of BUPA and had no way of making contact with them! I have been with BUPA all my life as we live abroad. The personel officer, nice Italian, just smiled every visit and said how can I help you? when he could do nothing! Separate department madam... We had a meeting with the Ships Doctor, she was just rude.
BUPA eventually paid me, some months later, but the monies went out of my account first, just aswell I had the funds there or I would have been overdrawn. The experience was so bad that never again will we sail CMV. Many people had the same experience. The ship was sick from Day 1 with coughs, colds etc. Perhaps they keep it going to keep the hospital busy??? (joke)
This past Christmas/New Year we sailed on Saga's new ship Spirit of Discovery. Wonderful, we are converts and will not be looking at CMV again whatever the price!