You can only cut a few surface roots before you affect the stability of the tree. Those bigs roots are the anchoring roots and cut too many, the tree becomes unstable. Feeder roots are smaller and you can't cut too many of those either.
I'd say consult with a licensed arborist on valuable trees.
They currently have a tree ring and it has been up rooted by the tree and they would like to up date it with a new flower bed but theses roots are above the gropund two to three inches four feet from the tree. the ring would be masive if they leave them and there yard is to small. it would be out or wack.
Best bet would be to remove whatever ring is there (block, edging, what?), and add 2-3 inches of composted leaves, then plant into the compost. Of course, mulch it too.
Adding soil over the top of the basal flare is generally not recommended, however, with only 2-3 inches of compost, you should be fine. Problems arise when you are adding more than that, and it's packed soil that does not allow drainage or aeration.