No, that is not what the Schindlers are arguing for. They share the same belief as other doctors who have examined Terri and believe that she can be rehabilitated. They also, along with Terri's friends who have known her all her life, do not believe Michael Schiavo's story that Terri said she did not want to be kept alive in a vegetative state. There is real reason to believe that Terri is not in a permanent vegetative state, as is being claimed.
As you are aware, the doctor who examined Terri (the one who asked her to follow the balloon on the video) spent 45 minutes with her and made his decision, which is the basis of all the court decisions. Contrast this with what the Nobel Peace Prize doctor said who examined Terri over a period of 10 hours. This is the Nobel Peace Prize doctor's field of expertise, and he should know who can and who cannot be rehabilitated.