That's exactly what the church is doing. All of this sophistry about the lawyers doing their job by arguing the law is missing the point. If the Catholic hospital really believed that those unborn babies were human beings they would not be taking this stance in court.
Only one problem with your argument, the defendants in the case were two doctors and the hospital. The defense argument that an unborn child is not a person was necessary as a defense for the doctors, and the hospital could not realistically deny the co-defendants of a cause for summary judgement. LINK
So the arguments that the Catholic hospital relied on a legal position contrary to church doctrine is not 100% true. The Catholic hospital most certainly befefitted from the legal position, but the argument was made for parties who did not profess to follow church doctrine.