The hubcaps moving is a "simple" physics thing. Not an issue of radials vs. bias-ply or flexing of the rim. Same principle as the "spinner" hubcaps you see nowadays. No matter how tight your hubcaps snap onto the rims, if they aren't physically fastened to it, they'll spin to some extent. Tire and rim turn - accelerating, braking, changes in speed, etc. - hubcap resists. The heavier the hubcap, the more it resists, full covers are more prone to this, too. Normal vibrations help loosen them up. Our car has steel valve stems, so we don't have an issue with the full trim ring damaging them, although I do remove them and reposition them so the stem is centered in the hole every year as part of my ritual when winter breaks. Only way to prevent it (or reduce it) is to increase the friction between the hubcap and the rim. I've seen strips of inner tube cemented to the hubcap where it contacts the rim work fairly well.