The most common causes of intracranial hemorrhage are 1) high blood pressure, 2) vascular abnormality, and 3) age related changes to the small outer vessels of the brain (protein build-up
making the vessels easily breakable). Other less common causes include a clot in a vein or a tumor.
Often, a CT is sufficient to make the diagnosis of a blood pressure related hemorrhage. If the bleed was deep - in parts of the brain referred to as the "basal ganglia" or "cerebellum", particularly in someone with a history of high blood pressure, often a head CT is all that is needed. However, if your dad has 1) no history of high blood pressure, 2)is 65 years of age or under, and/or 3) had his hemorrhage in an outer part of the brain, I often suggest doing further work-up including an MRI and possibly even a catheter angiogram (similar to the angiograms that are done for heart patients).
An MRI gives no "radiation". It uses magnets and radio waves, and is not thought to be associated in any way with cancer causing radiation. It is generally regarded as much safer than CT.
I don't want to disagree with one of your doctors. However, if the specialist in the city felt an MRI was necessary, my guess is that it is. I would probably go ahead and get the MRI unless your local doctor has specifically spoken with the specialist in the city, and they both agree that the test can be cancelled. An MRI is often very helpful at determining an underlying cause for the bleeding.