Amorphous materials at low temperatures: why are they so similar?

In addition to the well-known qualitative similarity of behavior of a wide range of amorphous materials, one dimensionless quantity, the reduced attenuation of transverse ultrasound, shows a quantitative universality whose explanation in terms of the standard "tunnelling two-level system" model would seem to require a totally unbelievable degree of chance coincidence. In addition, while the height of the "plateau" in the thermal conductivity is material-specific, the higher-temperature behavior is consistent with universal behavior. I sketch the outlines of a scenario which holds out hope of understanding these observations.