Try being a user of iMessage then switching to another phone without disabling iMessage in advance. Any Apple user who messaged you through iMessage will continue to send messages to a dead iMessage account.
I'm pretty sure I did this recently - it sent as an iMessage and after a minute or two when the message still hadn't been delivered to the destination phone it fell back on SMS (I'm assuming the iMessage registration times out after a while, though?)
I can confirm this happened to me a year ago and it was extremely frustrating.
I had to call back and forth from Apple/AT&T over the period of two days before they figured out what was happening and disabled it. Missed tons of messages.
uhhhh.... iMessage is opt-in and isn't enabled until you actively sign up for it in settings. You don't want it taking over your SMS & MMS - don't opt-in to it.