No, they're not the actual messages, just a log of what numbers the messages were sent to and recieved by.
The only way that someone can actually get the messages of what was sent or recieved is to subpeona the logs in a court of law. That's it.
I'm guessing dear ol' mom was bluffing to scare you into staying in line with the texting. Course, you could always try to talk her into an unlimited messaging plan, and you wouldn't have to worry about going over you messaging limit.