Hi-Ya ndnatty,
You didn't do anything wrong, and I doubt that your tires are mislabeled. Whoever originally put those 31x10.5-R15 Michelins on the 10-inch wide wheels erred.
According to tire manufacturer guidelines, those tires are too wide for those wheels. I ran into exactly the same problem with a Goodyear dealer.
Here is a generic table listing recommended wheel width to tire width.
Per the table, your tires should be mounted on 8 or 8.5-inch wide wheels -- confirming what the Sears guy was told by the American Racing Wheel representative.
If you look at your tires, you will likely notice there is little or no bulge in the tire sidewalls. With no tire sidewall bulge, your wheel rim edges and possibly the inflation valves are more subject to being nicked/damaged by curbs and rocks, just as Bounty mentioned in the post above.
Regards,
Gadget