Will Medicare/AARP pay for rehab services if the patient leaves AMA before services are complete?

My dad was discharged from the hospital and sent with his permission to a rehab center for physical therapy as well as IV antibiotics. After being there 4 days he wanted to leave. The main reason was he was tired of being cathed all the time. I explained that it was to help prevent him from going into kidney failure. I also explained that I couldn't take him home because I didn't have the supplies necessary to take care of him at that time. I tried to convince him to stay till Monday till I could speak with his dr.s. He still refused. He does not have a POA. So I tried and tried to convince him to stay and told him if you leave we are going right back to the hospital. He said he didn't care where we went but he wasn't staying here. So the rehab center had me sign for my dad and put POA, which I am not first of all. Secondly we got my dad in the car and took him straight to the hospital. Upon admitting him to the ER and testing we found out this: He was in AFIB, CHF and had pneumonia. The Dr. also said that it looked like he was trying to having a heart attack. They admitted him on Saturday and as of today we found out that he still has a staph infection, he has infection on his skin, they had to remove his picline that came from the hospital on his previous admission because there wasn't a dressing on it when I brought him from the rehab center to the nursing home, he was in AFIB, which has resolved itself as of today for now, CHF, pneumonia, had a heart attack and has a blood clot in his leg and a possible stroke which they haven't ruled out yet. So if he hadn't have thrown a fit to leave Lord only knows what would have happened to him between Saturday and today. So knowing that I took him from one faciility to a hospital to continue his care I would hope that would account for something.