To be honest, the Schindler's probably feel (rightly) that they have nothing to lose. So, if it takes a bogus religious interpretation or blaming the governor, they'll do what they can to get Terri fed again. They look bad because they look desperate and they look desperate because they are. They really don't care what we think of them.
They don't have the time to think about what others think of them right now. I don't think that ones religious beliefs don't matter, but that there may have been many other stronger arguments to be made. I just keep hearing about the violation of her religious beliefs and then the being denied due process, which is a more legitimate argument IMO.