Recommended via size for 0.65mm pitch BGA

I’m working on a PCB which I’d like to order at Aisler, but I’m facing some issues with the design rules (I downloaded your design rules for Eagle from Github and imported them).
Basically: Even at 0.1mm drill you’ll still end up with a 0.5mm via due to 2x0.2mm annular ring. This is simply too large for a 0.65mm pitch BGA, at least when using normal sized 0.35mm diameter solder pads. So my question is: Is/how is it possible to manufacture a PCB at Aisler which is suitable for 0.65mm BGAs?
Supporting 0.1mm drill and 0.4mm minimum pitch for BGAs is somewhat pointless if it’s not even possible to fit vias underneath a 0.65mm BGA. This is not exactly an uncommon pitch for BGAs.
Furthermore I’d like to ask if 4mil traces are doable. I have read the design rules and saw the minimum of 5mils, but sometimes the minimum is more of a recommendation instead of a hard limit, so figured I’d ask.

We do not support smaller Via sizes. You could get away with smaller traces, but it needs careful layout of the design, and we do not guarantee that it will work.