The output impedance of an amp has to do with the damping factor.
True. Damping factor is usually defined as output impedance divided into 8 ohms.
It has no relation to treble response.
Not true, in the case where speaker impedance is significantly different in the treble region than at lower frequencies.
If you look at the impedance curve that I linked to for the Focal Electra 1037Be, which I am assuming is similar to the impedance curve for Bryon's 1027Be, you will see that it is around 5 ohms in the bass and lower mid-range, and generally upwards of 10 ohms in the upper mid-range and treble region. That kind of impedance characteristic is not uncommon, btw.
For a given input voltage, an amp having negligibly small output impedance, such as most solid state amps, will maintain an essentially constant output voltage into that impedance as a function of frequency. Based on Ohm's Law, that will result in twice the amount of current and power being supplied into 5 ohms compared to what would be supplied into 10 ohms.
A tube amp, having relatively high output impedance, will not behave that way. The voltage that it "tries" to output will divide up between the speaker impedance and its own output impedance, in proportion to the ratio of those impedances. Therefore for a given input voltage to the amplifier, the amount of power that is delivered to the speaker at low frequencies will be smaller in relation to the amount that is delivered at high frequencies, compared to what a solid state amp would deliver. That will result in an over-emphasized treble.
If I recall correctly you have electrostatic speakers, which would interact with amplifier output impedance in exactly the opposite manner. The impedance of electrostatics decreases at high frequencies, so a tube amp would provide a treble response that is under-emphasized relative to what the response would be with a solid state amp.
Best regards,
-- Al