That makes sense now. Yes, that should work fine for you. The wire's overkill but as long as it's at least big enough for the application you're set. ie. Overkill is fine.
Offtopic, but FWIW what I think they're implying with the wiring size/etc is that the machine should be rated for 20A intermittent load, like a welder, where you could have a 30A breaker on 12gauge wire (even to the outlet if it's dedicated to the welder & your inspector is up on the code, whereas normally a 30A breaker would require 10gauge) due to the fact that the >20A draw would be sparse for the machine in use.
And yes, this is in both the CEC and NEC somewhere or other. There was a big debate over this some time back at one of Miller's forums, and it was shown that a) Miller specs it this way, and they quote the appropriate codes b) the NEC OKs it, and c) the CEC OKs it. However, getting that to fly with the local inspector is another matter...