Still see it as suspect, would be more believable if it appeared in the first post. If it did occur the pop would just be the battery case tearing open. And Apple does not make the batteries that are in iPhones.
No it was not set then extended. I had my battery replaced under the recall (actually the whole phone as my power button started to fail and I had AppleCare plus). The battery issue referred to in the program was for batteries that suddenly would fail to retain a charge it was no about batteries that expanded. It was set from the outset as 3 years from the original purchase date of the iPhone. I believe your only non-arbitrary date would be one day after you took your phone in.
It is a failing lithium battery and they do this sometimes not because of a "fault" but because the battery has reached end of life. They are not warrantied for life. If you have a real issue with this you might want to contact Sony who made the batteries for the iPhone 5. If you have only had the phone for two years from the original purchase then it is covered under the recall. Talk to a manager at the store.