Screen, if you have it then assess the situation. Some cancers are so slow as to not be a problem, some are not. There is a concern about over treatment.
Trust me on this. You really need to keep the old body's systems checked. It's analogous to checking the underhood fluids in your car.
Far, far better to discover that your enlarged prostate (yes, I am that old) is not due to an inoperable cancer. The one you didn't get diagnosed because you didn't mind peeing half a dozen times a night.
You are wise (and fortunate to be able) to trust your personal physician, but the bottom line is that YOU are ultimately responsible for your health, not your doctor. Sounds to me like he really cares about his patients.
Learn what the signs of prostate cancer are. I'm not a doctor, and I don't put myself out there as one. But 40 does appear to be too young. Since your dad had it, you might be at increased risk, but your doctor is right: that doesn't mean you'll get it. Still, know the signs. Have anything suspicious checked out by a licensed physician.