I'd say even for someone inexperienced in changing a tire, it would be pretty difficult to mount the spare "inside out" on the hub. It would be glaringly obvious. I don't know the op, nor do I know his or her skill set, but I'd bet that the wheel being on backwards isn't the problem.
I took some time when rotating my tires to check the spare fitment. I have the upgraded aluminum silver and gray 20's on my Laramie, and an 18" aluminum spare wheel. (Not sure what my window sticker says, if anything)
The lugs that come with it, have a cone that is .540" deep, while the face of both aluminum wheels is about .75" (very tough to measure with just a dial caliper). I got measurements from about .720 -.788", so I'm not sure if there's just that much tolerance in the wheel faces (I doubt it), or its just the crappy method and tool I was using.
I threaded a lug on without the wheels on and they just about bottom out against the rotor, certainly nowhere near .75" of clearance between the rotor face and the top of the lug cone, so any wheel that fits, should snug down nicely with plenty of force.
My Harbor Freight aluminum jack did not go high enough on its own to lift the front of the truck up enough for the wheels to come off the ground, so I had to use a stair tread as a platform for the jack... But it worked.
Also, with the truck lifted in Off Road II mode, I still couldn't slide under it on a creeper, because of the air damn, which is not the movable one on air ride trucks...
The spare tire itself says its for temporary use only, and it's not full size (width wise, overall height is close enough to the same nominally). It's a 245/70R18 (Ø31.5") tire. My normal tires are 275/55R20 (Ø31.9"). It also didn't look like there's too much tread there to be used up...
Sorry for the fuzzy pics, it was cold and I was shaking like a mf just holding the camera.
Also, just fyi, the torque value for the lug nuts is 130 Lbs-Ft, per the owners manual. I'm very much used to vehicles with torque values at 100 Lbs-Ft or less. Even my Tundra was 97 Lbs-Ft for aluminum wheels... Doing six lugs per wheel at 130 was tiring towards the end. I have the old school needle / bar type torque wrench, and I needed a short extension on it to get past the offset of the wheels, so holding the extension straight and then using the torque wrench properly was a bit of a struggle. Towards the end of the 3rd and 4th wheels, I had a system going that mad it a bit easier though.