You can get a copy of text messages from AT&T if you have saved the text messages on your cell phone or have them stored somewhere else.
But you cannot simply get a copy of text messages from AT&T from their servers unless it's deemed necessary by the law.
For example if the court grants a court order for them to get a copy of your text messages then AT&T can and will give the court a copy of the saved text messages.
But just anyone cannot get a copy of the text messages from AT&T.
Although AT&T and other cell phone companies do keep and store text messages and call records for at least 1 to 2 years they do not just give them out to even the people who have the phones with them.