FYI -- I work on this project, and I work with Roger Jones (the guy in the article), so I know a substantial amount about this.
Your definition of damping is quite right, but your definition of detuning is, in this case, not really what he means. What he means is taking a cavity, and changing its shape in order to "detune" some cells.
To explain:
The cavities are traditionally built in such a way that each cell rings (like a bell) at the design frequency of the accelerating rf. Since all of the cells are identical, the beam will excite exactly the same mode frequencies in each one (like a hammer hitting a bell). Since they are resonant with each other, they can and will ring coherently. Thus the amplitude of these modes will be proportional to N^2 (where N is the number of cells).
If they are made to have slight differences (detuned) that cause their resonant frequencies to be slightly different (but still within the bandwidth of each other due to their finite Q -- so they *can* excite one another), they will ring incoherently. This causes the mode amplitude to be proportional to N.
Thus, the amplitude of the incoherent ringing will be lower by a factor of N.
On top of this, they also add absorbing material to take out some of the power (the damping you refer to), and it is this that fits your guitar string analogy, not the detuning that Roger was referring to in the article. Absorbing material cannot change the frequency of the oscillation -- all it can do is remove energy from it, thus damping it's amplitude.
To go further, yes the differing stiffnesses of the springs under my car *does* look like a system of bells ringing at different frequencies. They are each ringing at a different "pitch" in order to detune any destructive vibrations. Your car analogy, including the absorbing rubber, is almost perfect! :)
I think the confusion is coming from the fact that this system can use both the absorbing material that fits your guitar string analogy, and the detuning technique that fit's Roger's bells. His analogy *does* describe the system very well, and I hope you can see that now.