1mm of paste is going to leave you with either a 1mm thick layer of thermal compound between the heatsink and CPU, which is a lot less efficient than having as much direct contact between the 2 objects as possible, or it's a lot of excess gunk that's going to ooze out over the side of the CPU.
The article contradicts itself. At first he says 1mm thick and then says so thin that it barely coats the surface. For comparison sake, a CD is just over 1mm thick.
A 1mm thick layer of thermal compound is definitely far too much.
edit: From emad's link to the Article Silver instructions: "Stock processors and/or heatsinks with normal surface irregularities will require a layer 0.003" to 0.005 thick as shown below to fill the resultant gaps". 0.003 to 0.005 inches is about 0.08 to 0.12 mm. So 1mm thick would be about 10 times as much compound as necessary.
KM.