Wow, this is suspicious for a number of reasons. Are you 100% sure you were in fact in touch with Apple? That letterhead does not look like the current AppleCare logo, and the wording of the text is strange. My guess is that your device got accidentally routed to their enterprise repair division, or at some point in your communication chain, you ended up communicating with a third-party repair organization that mishandled your order.
It's also surprising that they even attempted to reproduce the error in the first place. AFAIK, if your serial number is listed as an affected unit, Apple will change the battery no questions asked. What country are you in? Maybe Apple is operating differently in your region?