I'm no "source" to speak of, but did compete, in Decathlon plus HS, in plenty of those rings. Even had a clunky pair of Discus Shoes with a single spike up front to spin around. My current Asics Throwing Shoes have target-like concentric circles on the forefoot, as if you'd spin precisely there.
I seem to recall Jim Fuchs, Yaley OlyChamp reversing in the shot. There's always been a TowBoard so the reverse needn't be affected by the circle's surface. What it did change radically, in the ShotPut, was the ability to slide/glide a la Parry O' Brian, rather than hop like Fuchs. Hopping (sideways after swinging the leg forward) did put you in a decent throwing position; the main diff., besides speed, lies in the rotation (45 degrees more) while using the entire back that replaces the over reliance on lateral trunk movement (in the same plane).
In the same sense, increasing the Discus turn by the same 45 degrees, i.e. also lining up facing the back of the circle, went hand-in-hand with the concrete circle. Again, it allows greater speed w/o slipping, paradoxically permitting less friction at the turning foot w/o lateral slippage.
Then there's the all-weather effect, esp. post-rain when it's a lot easier to squeegee (sp?) out and towel off a ring than deal with mud.