Unfortunately you still don't seem to get it. Specific outdoors recreations are not listed in any of the access Acts over the past century as "allowed activities" and that includes camping, caving, climbing, walking, running, cycling, swimming, flying kites, sunbathing, picking wild berries, star gazing, etc, etc. The way all of the public recreational Acts work is to give a general grant of access, described as "air and exercise" in earlier ones, and "open-air recreation" in later ones, then to subtract the "forbidden activities" or "forbidden places" by way of a list of exceptions sometimes given in an attached schedule. In the specific case of CROW, you have no right to pick fruit or cycle or use a metal detector, or camp; you can sunbathe on a river bank or beside a lake but not "bathe" in it.
Camping, where it is not on an explicit "banned list" in an Act of Parliament becomes a local planning or specific park management issue. The Dartmoor National Park hasn't issued any byelaws to permit camping as byelaws are made to restrict things locally that would otherwise be legal. The Dartmoor National Park hasn't issued any byelaws to ban camping either, which would be pretty astonishing considering it has just spent a lot of money defending the camping rights that are implicit in the Dartmoor Commons Act.
In the case of Scotland, camping in the wilds is legal and acceptable so long as it is done considerately and doesn't interfere with other people's enjoyment of an area. In the case of the Loch Lomond and Trossachs National Park Authority, which runs a National Park for the benefit of all its visitors, and is the planning authority for its area, it decided to stop camping (other than on commercial sites or in campervans parked on public highway) at hot spots in the busy part of the year because it had reached a level that interfered with other people's enjoyment.
The important point you seem to have lost sight of in all this is that the Dartmoor case had to rule on whether being in an enclosed space stopped activities from being "open-air" ones as officialdom hitherto insisted was the case - to the detriment of caving. As the open-air argument was the main plank of WG/NRW/Defra's defence in the BCA's JR case, the defence position is now in ruins.