According to JOS on stiff-string synthesis, stiff strings (like on a piano) introduce inharmonicity (i.e. the harmonics of the tone are not all in tune) due to different frequency components of the wave travelling at different speeds. This inharmonicity is called "dispersion".
According to another page on the same site about modelling this effect, he says it can be done by putting an LTI (linear, time-invariant) filter of some sort at one end of the delay line (in waveguide modelling, a delay line is used to model a physical string) before feeding the output back into the delay line.
Somehow, this LTI filter introduces inharmonicity, or frequency distortion. But by definition, an LTI filter does not introduce any new frequencies into the signal (and thus can be accurately represented by a frequency-response graph).
How can inharmonic tones be introduced by an LTI filter? Am I missing something obvious? Do I not understand my DSP basics well enough?