<<But you need some kind of clothes, to protect your body from the bottle straps and lead belts, etc. >>
If you mean the actual diving gear he's wearing, that's not true. Plenty of people dive in warm water with nothing but a bathing suit on. Look at David and Gail at the beginning of the movie, for instance.
Now, you MIGHT need clothes on when diving on a reef or a wreck just to protect yourself from the things you might encounter underwater. There are things that can sting (leaving or a rash, or sometimes even killing a person) or bite, and on a wreck, you could get cut on any of a number of things. Of course, if all you're going to do is wear shorty wetsuit or a t-shirt, that's not gonna protect your arms, hands or legs, but I think wearing a more comprehensive wetsuit (ie jacket with sleeves, trousers, etc) might have been too warm, like wearing a parka in Texas in the middle of the summer.
So in fact, in terms of protection, Treece probably had the most sensible diving attire. Most of his body would be protected against injury, but without the excessive thermal protection a full body wetsuit would give. Of course, in the 80's diveskins became popular under such circumstances, but I don't think those were in use yet in the 70's (and besides, I think Treece would have been even less likely to wear a diveskin than a wetsuit).