My own father is a physican and very against any elective exams himself. His reasoning is that his colleagues are excessively interventive so the less medicine, the better. I wish your own father had been diagnosed in time but I can see the downside in doing too many exams as well. Doctors won't be able to keep their hands off treating any little lump they find, even if it's to your detriment.
Case in point, surgery for back pain causes said pains to worsen at about the same rate as it improves them.