I got a Best Buy to PM with a printout of the $9.98 price on toysrus.com. It also worked with a $5 coupon for Best Buy that I just got today on the shopkick app on my android. However it did not have the "Includes skin" indication on the front. However, later on I went in Walmart and was looking around, and the front one in the case DID say it included the skin. I wasn't going to bother returning at Best Buy and trying to PM once again at Walmart though.
So, if you really want that skin, try checking Walmart. At least at mine, they had less than or around 10 PSP games anyways, meaning they probably aren't that great sellers for Walmart. Seeing that did prompt me to get a copy of 3rd Birthday there, hoping the DLC code is inside of it. I have yet to open it to see though.