My brother just went to study medicine; they didn't get to CAT scans yet, but from what I saw he's learning about ECG, he is expected to understand the physics and math behind it on a basic level.
Doctors definitely understand how CAT scans work conceptually, to the extent needed to interpret the results, including whether or not the results are valid. They don't know, and aren't expected to know, how to build one, or open one up and fix it.