YBA feels that it is a real problem and that it can affect the sound. McIntosh also makes a conscious effort to avoid it happening by putting a thin layer of damping material between the heatsink and the chassis. I have also seen this in French Euphya amps. My personal feeling is that it probably has a bigger impact on the signal than, say, speaker cable lifters do. And some people swear cable lifters improve the sound.
Some amps' heatsinks will ring simply by being on with no one touching the heatsinks. This is due to the mechanical excitation coming from the transformers. Some amp designers pot the transformers to isolate them from the chassis so vibrations don't get into the signal. I know Karan does this.
Also, some amplifiers are designed with a massive chassis to dampen all vibrations. The weight of the casing in general will absorb any vibrational energy coming in or going out so that it doesn't get transmitted to the circuit (and heatsinks).
The easy way to stop the ringing of heatsinks is to barely loosen their mounting screws. If the screws are on too tight, the resonance frequency of the heatsink will rise into the audible range, which is what you are experiencing. It only takes about 1/8 turn to make a difference.
Incidentally, that is why every nut and bolt on a car has a specific torque setting that you must respect when tightening them. The vibrations from the engine and road will excite resonance frequencies of all parts and if the bolts are on too tight, they will vibrate and back off. The "sweet spot" is quite small in many cases. Same goes for your transformers and heatsink screws. I bet nobody told the Classe shop guys that they shouldn't wrench the screws on as tightly as possible.
Arthur