This computer tech is clueless. Each thermal compound (pad or grease is an impediment to proper thermal flow from core to heatsink). They are only designed to fill in the natural microscopic valleys and grooves in the two surfaces (places where there are air gaps - air is a terrible thermal conductor). If you have a thick layer of them, they can actually become thermal insulators and give horrible results (which is what the two together would do). Quality thermal greases/pastes are better than pads because you can make the layer between thinner. Pads have to reach a certain temperature and then they melt to become thinner, but don't get as thin a layer as greases can.
Edit: This
website from Arctic Silver explains better than I did what the thermal interface is.