My wife's Cingular 8125 (made by HTC) did exactly the same thing. It would almost always send double text messages. I had the exact same phone, and it never did it. We called AT&T (Cingular) several times and reviewed the account settings and such, but they could never do anything about it, other than "update the software on the phone via a download", which did nothing. When we got iPhones, we gave the 8125 to our daughter and switched to her SIM card. It did EXACTLY the same thing, double sending text messages.
So the problem does indeed have to be a faulty phone. Given that the account settings are for a specific phone number and yet it still did the same thing after switching SIMs (and therefore phone numbers and account settings), tells me it has to be the phone. We replaced the 8125 with a cheapo flip phone, and it hasn't double sent a message since.
If it were me, I would insist on a new phone; after all, you are being charged for double text messages, as are your recipients. The reason we didn't replace my wife's was because it didn't start exhibiting the problem for several months after purchase, and by that time, the only replacement option was a refurbished model (and she has some built-in resistance to such items).