I think we need to be just a little more trusting these days, people...he just may be telling the truth.
I had a similar thing happen with a very expensive item I shipped to my brother via UPS. The item was supposed to be signed for, but instead the driver left it under a bush in my brother's front yard. Yeah, under a friggin bush. The driver even left in the notes on the "missed you" slip slapped to the front door that the package was right there in the bushes! Doesn't take much for an item to be taken at that point...luckily, my brother arrived with it still there, but both of us were blown away.
I've dealt with a lot people in shipping and receiving, and it's back-breaking work. What's worse is if the driver gets a 'split' where he has to take things from another driver and deliver those on top of his full truck. So it wouldn't surprise me if a tired driver said the hell with it and left it there. Just bad luck that someone nabbed the package.
The responsibility goes to whomever is the primary shipping party. If Woolworth's uses their own shipping, then they're responsible. If they use a third-party courier, then that courier is responsible. Either way, Nintendo is not at all responsible at this point. They shipped to the Woolworth's warehouse, and after that it truly becomes someone else's responsibility. I feel your pain, and I would never say don't try but I don't think Nintendo is going to say anything different than contact Woolworth's or the courier company who delivered your Wii.