It's really likely there was a date and it was over four years. I don't think I've ever seen one without a purchase date and is something I always check as it's crucial to know for things like warranties, APC+ and consumer law etc. It's super rare for a whole Macbook to be replaced under warranty as they always want to repair with as little parts as possible so I'm not 100% if the purchase date is carried over or the refurb date is used.
You could now take it anywhere authorized and get it repaired if you wished as what they've done is applied a code to the serial/machine due to their mistake. This specifies the keyboard should be repaired free regardless of warranty and eligibity provided the customer hasn't modified it or something. They're really good at owning up to their mess-ups or giving a bit of leeway if you were a few days out or something
You can also insist that you want to use the mail-in repair strategy (send to the repair center) and have it delivered back to you if you'd prefer that. The fact you're having it repaired under a code should be irrelevant to what strategy they use.