Hey Rick,
There's another aspect to the input cable sizing... That's noise being introduced when dimming highly-capacitive loads (as, apparently LEDs are). When the SCRs turn on in mid-cycle - like when the dimming level is somewhere around 50%, you'll be sourcing a *lot* of current for a very short time - basically a current spike. This spike will go to the supply ground wire (this is all fine & within spec, etc).
The problem comes up when the ground wire is small (acting as a small resistor)... The voltage on the ground wire, which should remain at or near zero, will "bounce" when it sees that current spike. Depending on the design of the controller electronics, the amount of filtering in its power supply, and the susceptibility of the individual components, false triggering of outputs (or worse - to the extent of possible component damage), could result.
I've seen some discussion on other forums about erratic channel operation (though I don't think it was for RJ's Lynx devices). I suspect a lot of this is due to this "ground bounce" effect on "undersized" power feeds.
Not saying that this is a problem for you - just one reason to use reasonably sized supply wiring (beyond what's theoretically required to supply the rated current for the lights).
--Dave