I have been running radials on my '57 T-Bird since 1973. In years gone by I have driven the car on long distance high way trips through out California and Nevada and have never had a hub cap come off.
The full disk hub caps are prone to coming off during tight high speed turns or if a large bump is encountered, however, the style of the tire has no bearing on the loss of hub caps....
This is one of those old tales like thermostat's or no stats making engine run cooler and non-detergent oil being better for old flat-head, etc., engines.