As you correctly state, bump-ball interconnection resistance depends - apart from the vias' resistance - on material and bump diameter. Generally one can say, bump connections are thicker and shorter than comparable wire bond connections: e.g. a 25µm thick and 1mm long gold wire can be used for up to 400mA. A 75µm diameter gold bump on the same pad size of course is much shorter (50 .. 100µm) and its heat transfer is much better, so could stand a lot more current (order of ampères).
In such case, the current more likely is limited by the vias' resistance, I think.