Patrick,
No. You're not wrong.
Texting, to me at least, is just like phone calls. Most work places limit personal phone calls. We do in my office. An emergency is, of course, a completely different matter. But just routine run of the mill phone calls/text message are a different matter all together. Tell him that you're paying him to work, not text. He can text on his lunch hour or his break (if he gets a break).
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