The scene has a transparent background and there is camera preview behind it.
I tried scaling. It did not help.
I asked our designer to scale down the model and now it has such properties:
bounding box : [-56.823803, 54.82773, -113.101685, -20.355627, -29.19638, 7.774193];
transformed center : (-0.74186236, -83.03801, -14.0675335);
origin : (0.0, 0.0, 0.0).
Camera position is (0.0,-66.72865,-168.31546) now ant it looks at (0.0,-66.72865,0.0).
Calling to wasVisible() returns true without any additional transformations (no scaling, no translation). And object is still invisible...