1. Find a deal like this one
2. Buy the exact same product at a competing site that actually had it in stock at regular price.
3. Quickly go back to the site with the sale/price mistake and take a screenshot of the lower price.
You screenshot will now have a later time that your purchase time.
Also submit it to web.archive.org as another reference that it was on sale at that time.
Basically the price mistake still needs to be viewable online after you make your order on another site.