Tire Pressure - but wait... a different question!

Air pressure is measured by the amount of compacted (density) air inside a vessel (tire) compared to the air outside the vessel. Anything that reduces the volume of the vessel (tire) would therefore increase the pressure.

Therefore, the answer to the question boils down to, "Does the inside of the tire (its volume) become smaller when it is carrying a load?" If yes, then your co-worker is right. I actually think the tire retains the same volume but in a different shape.