I was going to just mod you up, but I figured your post would soon be at 5 anyway. (if not, mod parent up!)
Yes, you're absolutely right. Lots of bad physics and a completely incorrect conclusion in that article. If there is an improvement in the thermal interface, the heatsink should get HOTTER. All of the heat goes somewhere. That's the first law of thermodynamics... conservation of energy.
You can break it down to a thermal resistance model which is functionally equivalent to an electrical resistance model. Difference in temperature is the "voltage" that drives the flow of heat (current). The heat (current) is a fixed value. The resistances are the various materials the heat has to flow through to get to the air. It can take many parallel and series paths to get out and you can build a resistance network to calculate heat flow through each "path". One way is through the IC leads, into the board, and eventually to the air... or the most direct path is through the heat spreader, through the thermal interface material, into the heatsink and eventually to the air. If the heatsink reads a lower temperature, that means less heat is flowing through the heatsink and that heat is taking a more difficult path to get out and thus the IC junction temperature is HIGHER. That's BAD.
So yes, the math doesn't add up. The thermal interface between the IC and the heatsink should be spread so thin that the thermal resistance across it is almost negligible. Thermal grease is only there generally because it's it's much higher conductivity than air and if you don't have it, all you have is air in all of the little surface imperfections of the heatsink and heat slug on the IC. Adding solid particles to the grease only serves to hold the heatsink and IC heat slug further apart, so even if it's great conductivity, it's generally the wrong thing to do.
-S