None of the debaters who support the idea that different tones can be produced independent of the speed of the hammer have offered specific "additional noise" except the key hitting the key bed. If you move the key down at a certain speed it doesn't matter when you release it- it's going to hit the key bed. It is conceivable that if the finger is still in firm contact with the key it may produce a different sound from that impact than would be produced if the key were freely rebounding, but beyond that what else could change? What does your tuner mean, Dima, by "a different sound spectrum"? Is he arguing that the "additional sounds" are creating interference patterns with the strings' sounds? That's not altogether unreasonable, but, again, what are the additional sounds? Unless a player has sticky fingers there's no way of pulling back the key that has been set in motion, so the key bed will be hit if the key exceeds a certain speed.
I don't have the passionate feelings on the subject some have expressed here, but I tend to agree with Ax. At the same time I suspect that all the various ways players have of striking, even "yanking" as Dima mentions in her last post, are simply physical representations of their mental approach, and these physical representations better allow them to maintain a continuous mental connection to the sound they intend to produce.
Has anyone seen a chess player screw the bottom of a moved piece down into the board? He or she is effectively saying, "This is a move about which I have no doubts," but she's saying it both to the opponent and to herself. The physical action creates the mental state, just as the mental creates the physical.