Private car sale


I have a question about a private car sale. I have a loan for a car that is a private sale, The bank required me to give them a copy of the registration card for the car and that is who the check is made out to. After I rec’d the check I noticed another person on the registration then I have been dealing with apparently the car is in the persons fiances and old boyfriends name. The boyfriend is going to sign a power of attorney for the car so that the girl can do all of the paperwork. My question is this they want me to give them the check to pay off the loan and once the title is cleared get it reissued to just her so that I can get the title transferred. I do not feel I should be giving any money to pay for a loan to pay their car off to get my title. I do not want to get into a legal battle at all. Cant they get the title changed while the loan is still active? Why does it have to be paid off to get the title changed?