It's fluid dynamics. He has a point that cooler air (denser) is more resistant to flow so will create more pressure loss through the exhaust (all things being equal).
You are confusing this with absolute pressure/density which something like Boyle's law describes for a given volume.
The 'zaust outlet on the engine 'sees' the sum total of the pressure losses through the exhaust system plus one atmosphere, not the pressure of an idealised gas where volume is held constant as temperature is increased. Pressure loss is government by viscosity, temperature, compressibility and density of air plus the friction factors and internal diameters and profile of the 'zaust system.
All things being equal:
Fat 'zausts = less pressure loss.
Thin 'zausts = more pressure loss.
How temperature loss of the 'zaust gases through the system (and the corrosponding increase in density) feeds into the equation I am not sure. It is certainly possible for a very cold, dense 'zaust gas, passing through a fat tube, to create more pressure loss than a hot, less dense 'zaust gas, passing through a skinny tube. Of course more pressure loss actual heats the 'zaust gas back up through friction, equals less density, so this is very complicated full of non-linearities and feedbacks.
If you were a geek you could mount a pressure transducer in the 'zaust manifold and measure the pressure losses through the system.