You're crazy ... but you still may be right.
I came across this in measuring:
It appears that the LCD-2 is storing a little energy, and releasing is some 400uSec later. The second bump on the 300Hz square wave, and the little lump of wiggle after the spike on the impulse response may indicate what you guys are talking about. 400uSec is not a long time, but it is about the timescale of the inter-aural time difference between ears with a 30 degree off axis speaker, so it's right at about the timescales that are used for localization, and I would expect your brain is able to make something of the artifact.
Whether this is the source of the "reverby" sound, I don't know, but it's possible.