Why is the floor always tiled?
Both readings have something in them. Memphis — Ettore Sottsass's 1980s Italian postmodern movement, all bright laminates, squiggles and asymmetry — was absorbed wholesale into the genre's pattern language. And a repeating high-contrast grid is the clearest possible way to show a plane receding, which is why the checkerboard recurs through early 3D work.
The mall-lobby and tropical-leisure vocabulary that surrounds it — tiled floors, indoor palms, fountains — comes straight from 1980s advertising and city pop cover art.
What the tile does in practice is architectural: it establishes an interior. A gradient sky with a grid under it is a landscape; the same sky over tile is a building with nobody in it.
No single origin is documented for this motif, unlike the Helios bust or Nagai's palms. Anyone telling you the checkerboard came from one specific source — a particular demo, a particular sleeve — is going further than the evidence does, and so would we be if we named one.