DDD
I belive he trusts you fully.
I have two that will sleep like that - Pootie and Casper. Pootie has NO SHAME whatsoever. Legs splayed out like a broken pair of plyers. Casper upon waking in that position likes to be powdered (he's white with sensitive skin and belly breaks out) so we put baby powder with cornstarch on his belly and bottom. He can almost get his back legs up to his ears - it's hysterical to watch.
The other Pit bull will never EVER be found on his back. In his mind he's the Alpha and won't take a chance that someone could "get" him. Occasionally I see him sleeping on his belly with the pads of his back feet up; and when I see that I know he's relaxed. It's a shame he stays wound so tight the rest of the time.
I'm watching 2 puppies right now and they both came to the house as balls of biting, unpottytrained, boundless energy. They both now sleep on their backs, snore, are housetrained and we're working on NO BITE. But they're enjoying being on a schedule.
I think they're leaving this week - I'm glad I'm getting attached.