Plot3D is incorrectly returning "1/0. encountered"

The best approach for plotting over non-rectagular domains is to use the regions form of Plot3D:

 Plot3D[1/y, Element[{x,y}, Parallelogram[{0,1},{{1,1},{0,1}}]]]

The problem is also present in Mma v 9.0.1 to 10.3 in Windows.

Wolfram Technical Support contacted. Support case with the identification [CASE:3445899] was created.

This does not solve the problem, just adds to the diagnostics.

The function get evaluated symbolically and at {0.0000715,0.} before starting to canvas the PlotRange.

f[x_, y_] := Block[{},
  If[
   Not[NumberQ[x]]
    || Not[NumberQ[y]]
    || Not[0 <= x <= 1]
    || Not[1 < y < 3]
   , Print[{x, y}]
   ];
  x]

Plot3D[f[x, y], {x, 0, 1}, {y, x + 1, x + 2}]

but