Ground moisture alone would be an issue with Ditra on top of the wood. Putting poly under the foam doesn't change that much either- the wood HAS to be allowed to dry toward the room, since it has ground moisture drives that can only be mitigated, not 99.99% blocked. The channels need to be positively vented to the room air to change the long term moisture picture for the wood, since it won't pass moisture by any other means due to it's poly layer. Simply venting moisture into the channels does squat if it has no place to go.
Fasteners punching a bunch of holes doesn't change the vapor barrier aspects of poly. The fasteners aren't vapor permeable either, and with vapor diffusion it's all about the available cross sectional area anyway- what's the cross sectional area of all the fasteners as a fraction of the whole? What's the cross sectional area of all of those micro-tears in the poly surrounding the fasteners? (Answer: Not much!) Even if 1% of the area was holes it would have to be tiny holes on a very tight grid to allow much drying capacity. Perforated radiant barrier foil products are ~2% holes by area with tiny holes on a 1/4" grid and they still come in at under 10 perms. Any wood more than an inch away from the defect in the poly due to the fastener doesn't get any drying relief worth mentioning.
According to the spec, the permeance of
Ditra is 0.006perms,which is as vapor-tight as it gets, a true vapor barrier. It's designed to protect the tile from moisture drives coming from below, not to protect the subfloor from spills on the tile or other moisture drives from above the floor. (Tile is usually porous even to liquid water, and usually relatively high permeance even compared to wood.) Ditra is really the right thing to provide the mechanical decoupling needed with a radiant floor, and it would be fine over a wood subfloor that had the capacity to dry downward, but good luck with downward drying on a basement slab. The only sure-fire option here is to limit yourself to materials that aren't susceptible to moisture under the Ditra.