Usually in both Home Depot and Lowes they carry a stack of 'premium' 2x4 and 2x3 that are supposed to be kiln dried. I've had good luck using these so far, and they aren't much more then the green 2x4. They are sometimes damp, but not quite the sopping wet that the rest of the lumber typically is.
I sort through the pile and try to find fairly straight pieces with decent grain - look at the end of the piece, if the grain is C shaped, there is a good chance the piece will cup as it dries.
Looking at the pics and reading the blurb in the initial link, it looks like the guy is using 2x4s built out of plywood (also mentions engineered lumber). sounds way too expensive...
Here's a pic of a 40B stand I've recently completed (I still need to finish sealing it), built almost entirely of 2x4 and 2x3 lumber