Doing the same thing in a 58 year old basement with dricore (local supplier called SubFlor here in Quebec, Canada). Their website has instructions on framing either outside or on top of the dricore.
If you choose the option to put the framing directly on the concrete, make sure you put a foam sill gasket underneath the wood.
After a sewer backup/flood in May, I had to redo my basement bathroom. I will be using a mix of BluWood directly on the concrete pad (with foam sill gasket) and on the dricore (SubFlor) with screws that do not breach the OSB top (framing depth = 1.5inch plus .5inch into SubFlor).
I have had the SubFlor installed for 3 months (I work on a limited time budget - my wife is p/oed that I really take my time on projects
) but the upside is that I can confirm that it has completely eliminated the efflorescence whcih was there previously with tar paper under (rotted out) 2X3 wood framed subfloor - plus I gained more room height (SubFlor = 7/8 inch, previous 2x3 sub floor + 1/2inch plywood = 3inch, net gain = over 2 inches).
Whichever, don't forget the 1/4inch expansion gap around the dricore and the caveat about wrapping the vapour barrier.
Pictures attached (first = new dricore, second and third = rotted plywood in old bathroom, fourth shows new plumbing rough in) - framing will (hopefully) be done this weekend - will post pics later.