In conifers USFS rated climbers can climb without rope attachment in certain circumstances.
Just so I can't stop wincing when I read 'free' climbing. You are indeed talking about free climbing when no gear is used to AID the climb. Rope for fall protection doesn't effect whether you are free climbing or not. Free is just using your natural climbing ability, rope or no.
When you do it without fall protection you are climbing 'solo'. The kind of climbing your talking about when you just climb a tree kid style is technically 'free solo'... although with trees I prefer 'kid style'.
Kid style is the coolest way to climb but it's also the most dangerous, all other things being equal.
3 points does NOT guarantee safety. I know of someone who had four points when a limb she was standing on snapped, she fell and fractured her spine.
Like all rules, 3 points is a good starting point, but it's not hard and fast, it's a guide. Anybody that climbs rock knows that it's not unusual to be on a single, sketchy point.
Climbing is VERY natural thing for humans, we were arboreal for eons. Just climb the damn tree.