Can't send/receive texts without data turned "on"
I cannot send or receive a text message (iMessage or SMS) while my data is turned off. I currently have it turned off because of a glitch with my data going over for no reason and AT&T will not offer any help. They told me numerous times that data is NOT required for texts but cannot tell me how to fix it. I only have problems with other iPhones (dad's texts from android send immediately). I've tried wiping the phone and changing every setting possible.
Any suggestions??
**note: I have not updated to iOS7 but had this problem prior to the update being available
iPhone 5, iOS 6.1.4