Keros pretty much nailed it. These mechanics that you're talking to are just flat out wrong. These trucks were not "designed" for a specific size wheel. An overall tire circumference maybe, but not wheel size. And this has to do with things like speedometer calibration, tire clearance and things like that. They come from the factory with 16", 17", & 18" wheels, and if you're in the Southeast region like me, there is even a port installed package called the X-SP, that comes with 20" wheels. Also as calikev pointed out, the 5th gen Limiteds come with 20" wheels.
You'll notice a different road feel because you're swapping out rubber for metal. This equates to a rougher ride, but you'll also get improved steering response because a shorter side wall will have less tendency to deflect. Back in the day, the tires were a lot bigger factor in the suspension design but the suspensions and tire technology is a lot more advanced now.
Also a great point Keros brought up was how 20" rubber hit's you in the wallet. Trust me, I know. But look at every truck line out right now (or even car for that matter). You'd be hard pressed to find a model that doesn't offer 20" wheels at least as an option.
So in summation; I have big wheels because I like the way they look. These are not the best option if you plan on wheeling the rig. Rubber is expensive. Bottom line, if you want the 20's, then keep them. From a mechanical engineers' point of view. Hope that helps.