Welcome to the world of modern technology! Good grief, when I was kid - our modern technology consisted of pressing 'record' on the VCR while watching the program you were recording! ha!ha!
As for your son...I agree with your husband about if he hasn't given you reason NOT to trust him, then you should trust him for now.
I DO believe you need to set boundaries! Maybe the time he can have it, allow you to view the phone whenever you want, etc.
I wouldn't worry about him deleting his text messages, I do it periodically myself. Not for any reason other than thinking I didn't need that one or I already went to that appointment, etc.
I know there are some cell companies that allow you to view text messages, even if they've been deleted. I guess you would have to check with your provider.
I have a 16 year old and she has hung herself many, many (many) times. However, this past year, she seems to have gotten it right and she is allowed a little more freedom. But, she knows if she loses that trust with us - she is back to Square 1! And in our house, Square 1 sucks!!! :)
I wish you the best...