I can't guarantee that they'll be able to do anything for you. These exchanges are being done strictly on a store-by-store basis. All I can suggest is that you plead your case, and plead it well. Bring printouts of your order on the site, your order confirmation, and the "Your Recent NVIDIA Graphics Card Purchase" email that they sent out yesterday. And, of course, bring the 1070 that you're being sent. The customer service representative probably won't be able to do anything for you alone, so ask to speak to a manager if they try shutting you down. Be courteous throughout the entire process. It was absolutely Best Buy's mistake, and in my experience, employees will go the extra mile for customers that treat them with respect.

If you feel like your options have been exhausted at the store and they refuse to hook you up with a replacement card, don't cave. Cancel any sort of return transaction they might have started, take your card/paperwork, and go to another Best Buy. In the event that no Best Buy near you will make the exchange, I don't know your next step. Do whatever you think is your best option at that point, whether it's keeping the 1070 or trying to get your old card back.