Ok. So the 16's I got did not fit. They came off a 98 Tahoe or something close to that. Apparently 16's will fit, but not that year for an '03 Denali. They have a different back-spacing (is that the same thing as offset?) so they hit the brake calipers.
I'm pissed. Got good 16" tires, just paid to get studs put in them, and now I have rims that won't fit the truck. Sooo, be careful if you are looking for 16's. Some fit, some don't. Make sure you get the right ones. I have to now figure out how to pay for another set of rims, then swap the tires over to those, then put them on the truck. Turning into a bit of a PITA.