I have an iPhone 4 (iOS 7) with cell plan but no data. When texting with non-iPhone users, I get the texts to and from no problem. When texting with iPhone users, though, the messages will only appear when I'm on Wi-Fi. It appears that when iPhone users (like my wife) try to send me a text message, it defaults on their end to iMessage, and those messages won't appear until I reconnect with Internet.

I can send text messages to everyone at any time no problem. Shouldn't messages that can't go through as iMessage be delivered as text? Do I need to delete my Apple ID from Messages to ensure that it only attempts text messages (but then I won't be able to share pictures/etc. via Messages when I AM on Wi-Fi)?