I am puzzled by your results. There is a difference between bread machine yeast and active dry yeast, but little difference for all practical purposes between bread machine yeast and instant dry yeast. Bread machine yeast and instant dry yeast can be combined directly with the flour, whereas active dry yeast requires proofing in a warm liquid.
Depending on the recipe or formulation one might use, the dough may or may not rise that much during refrigeration. If it is a low-yeast, cold fermented dough, you might not see much rising of the dough until somewhere between the second and third day. But, even after a day or so the dough should be usable after letting the dough warm up for a reasonable period before using to make a pizza. If your dough temperature going into the refrigerator was on the low side to begin with (e.g., as a result of using cold water), or your refrigerator operates on the cold side, or your room temperature was on the cool side, any one of these factors could have affected the rising of the dough. But I don't think it was the bread machine yeast that was the villain, especially if it was viable and not improperly used.