I just saw the commercial again today. It makes you wonder. I know the individual stores are their own separate profit centers that can set their own prices according to their own overhead except for the nationally advertised sale prices.
I live around 5 sears stores and the in store items may be priced differently depending upon the size and location of the store. They all will honor sale ad prices but not all of them list them and you have to show them the sale bill. Good luck.