I think the implication is that under this tented tensile structure you could build whatever radiation shielded (or not) structures you wanted, and this just contains the air.
Radioactive particles (dust) in air are problematic. The gas in air does not become radioactive (at least in a dangerous way) from exposure to radiation.
If the surface of mars is exposed to radiation capable of making particles become radioactive, does that mean the surface is already radioactive? Or would this only happen to airborne dust particles, not to sand particles on the ground?
If you're breathing silica dust you're going to get silicosis anyway, so there's not much point worrying about it.
Maybe the living area buildings inside the tent can have a vestible / "dustlock" for keeping the dust outside, and outside those it just becomes standard to wear a dust mask.
If you’re putting all of your eggs in the “shielded other structures” - why have the other structure in the first place? It’s not as if you can live outside those “other structures” if you’ll just die of radiation poisoning.
Or, to put it another way, any structure capable of shielding against cosmic radiation should be capable of also holding air (we’ve gotten really good at that).