There is a fix posted for this issue where you do not need to turn off vibrate or turn off view in lock screen. Go to the following link to read it. http://iostricks.com/double-text-message-ringtone-fix-iphone-4s-and-iphone-4-131
I had a the issue on 5.0.1 and after updating to 5.1.1 it was ok for about 1 week and then the problem came back. This is the only solution i found that works best so far.