The website says that resampling will ruin the photos when they are printed but they look great. Wont just resizing the image make it lower quality as well?
Is the overall flow that you provide image(s) to Society6, and they print them when a customer orders one or more of your images? If so, I agree with their statement not to resample, just send them images at their full/original pixel dimensions. If they are doing the printing, it's their job to set the resolution to get the best result from their printer.