As was already mentioned - the warranty dates that you show are estimates of the date of purchase.
If your original bill of sale/receipt is a different date, then you need to contact Apple with that proof of purchase.
Apple will adjust that date for you.
OR, that would be one of the "perks" of obtaining iPhones through dodgy sources.
Absolutely sure. They wouldn't let me leave the store without them activating it via their POS device. As soon as they did it, my old phone was inactivated. And the cellophane plastic wrap was still on both my just purchased iPhone 6S+'s.