Yup. If you trust them to text, you trust them to text. If you don't, then you use parental controls to completely disable texting.
Or do what one acquaintance of mine does: His sons are allowed to do whatever they want, but if they ever "hide" what they're doing when mom or dad come by, it gets taken away. The computer is placed in a hall so that the screen is visible from just about anywhere - if they feel comfortable browsing the Sports Illustrated swimsuit issue with their mom looking over their shoulder, so be it. But if they close a window the moment mom walks by, no computer for a week.
Same with their phones. Mom & Dad can, at any time, ask to see what's on their screen. If they don't show, it's taken away. But if they're fine with the parents seeing it, they can do it. They had one incident where the 15 year old had a topless picture on the screen, and he turned beet red, but showed it. They're pretty sure he made a point of not doing it any more. (They also aren't allowed to have their cell phones in their rooms. The chargers are in the dining room.)
That could quite honestly be the most ridiculous thing I've ever heard of.