This doesn’t sound right to me. Certainly radar can, at certain bands, see through foliage (so-called FOPEN). I don’t have familiarity with radar seeing through buildings at the sorts of ranges and coverage rates that you’d want to use for ground mapping.
The article references the Shuttle Radar Topography Mission, which should use C- and/or X-Band radars — both should see returns from foliage and buildings.
Without digging more into it, my thoughts about the reason behind absence of foliage and building shadows in the radar data are potentially: 1) resolution of the radar data is too low (tens of meters or more), 2) maybe post-processing of multiple radar passes with different geometries to get rid of them, 3) steep grazing angles from the radar not generating much shadow to begin with.