Wammers, yes that sounds bang on, strange that the exhaust gasses cool the combustion process, always thought the exhaust gasses were raging hot!!
Grrrr may give the expensive fuel a shot, but I think it's a little more complex
Less air, less oxygen, less heat. Exhaust gas replaces oxygenated air not needed to maintain the power level requested within the bounds of EGR operation. If the EGR is open at an high power request, and exhaust gas enters the system, there is not enough oxygenated air to burn the fuel needed for that power level cleanly which results in smoke.