Note that FM radio is also bandlimited, in fact it has a lower limit than CD (only 15 kHz instead of 22.05), and is more comparable to digital audio sampled at 32000 Hz. Not to mention, chances are that music on FM radio is played from a CD format source anyway.
However, it also uses pre-emphasis/de-emphasis, so the maximum amplitude of treble frequencies is limited, and FM radio broadcast is often subject to different equalization and dynamic processing than CD. Because of the more limited high frequency response, it may sound smoother and less harsh than digital audio, but that does not mean it is more accurate. The main culprits when it comes to harsh/unnatural cymbals in CD audio are probably transducers with uneven and peaky treble response, and badly mastered CDs (they often have boosted treble to sound better on lo-fi equipment, and when you combine that with heavy clipping, and listen to it on a headphone that has a 10 dB treble peak, it is not surprising that the result is not quite pleasant).