Why does the InterpolationPointsSubdivision method fails to calculate this integral correctly?

Question

Consider some dataset.

I use the following code to interpolate it:

SetDirectory[NotebookDirectory[]];
dataset1 = Drop[Import["dataset.txt", "Table"], 1];
yxDistr[y_, x_] = 
 Interpolation[dataset1, InterpolationOrder -> 1][Log10[y], Log10[x]]
xmin = 10^-1.98;
xmax = 10^4.98;
ymin = 10^-7.28;
ymax = 10^0.497;
xMax[y_] = 
  Piecewise[{{4000, 0 <= y < 10^-3}, {3000, 
     10^-3 <= y < 2.5*10^-3}, {2000, 
     2.5*10^-3 <= y < 3.5*10^-3}, {1500, 
     3.5*10^-3 <= y < 7.5*10^-3}, {1000, 
     7.5*10^-3 <= y < 0.025}, {500, 0.025 <= y < 0.04}, {300, 
     0.04 <= y < 0.07}, {200, 0.07 <= y < 0.1}, {100, 
     0.1 <= y < 0.25}, {50, 0.25 <= y < 0.5}, {30, 
     0.5 <= y < 0.8}, {20, 0.8 <= y < Pi/2}}];

Here, xMax[y] denotes the maximal value of x for the given y (I have obtained it by hand).

Next, I want to compute an integral over x and y within some interval $ymin<y<ymax$. I introduce the following functions:

ySpectrum[method_, yminv_, ymaxv_] := 
  NIntegrate[yxDistr[y, x], {y, yminv, ymaxv}, {x, xmin, 4000}, 
   Method -> method]
ySpectrum2[method_, yminv_, ymaxv_] := 
  NIntegrate[yxDistr[y, x], {y, yminv, ymaxv}, {x, xmin, xMax[y]}, 
   Method -> method];

If using method="InterpolationPointsSubdivision", ySpectrum["InterpolationPointsSubdivision",0.2,0.3] gives zero, while ySpectrum["AdaptiveMonteCarlo",0.2,0.3] is non-zero (as it should be, if looking at the initial data). I may improve the accuracy of the prediction of the "AdaptiveMonteCarlo" by calling ySpectrum2["AdaptiveMonteCarlo",0.2,0.3].

But how to make "InterpolationPointsSubdivision" work correctly? It does not work properly with non-rectangular regions of integration.