When the doctor is showing an X-Ray at the beginning of the scene, she puts the exam backwards, meaning the right side is on the left, thus changing the position of the heart - a mistake any med student would notice. She also says that there are several lesions in the chest, whereas the x-ray appears to be normal from the distance the viewer can see. Additionally, an x-ray is not the best exam to identify this kind of cancer, it would usually be a CT scan - an exam available in the time the story is being told.
At the beginning of the movie the doctor tells Griffin that he has like 12 to 14 lesions in his lungs and gives him about 2 years to live. It might be possible to extend his life that long, but only with chemotherapy and/or radiation therapy. But if Griffin was that far along, and he did not get any treatments, he would surely be weak, tired, coughing, weight loss etc... later on in the movie. The disease would start to worsen sooner rather than later.