Hi Alpay,
Thank you for your patience, the quality assurance team have got back to me and they say that the vias are tented but the solder mask is just a little thin. This is within IPC-class 2 standards however and about 30% of boards will come out like this. For BGA via tenting, they suggest soldermask filling to ensure they are fully covered, otherwise smaller drill holes should help with the tenting.
On another note, I think if a paste/reflow method was used to solder the BGAs then the boards should still be workable. The stencil should only allow paste to be applied to the BGA pads and the soldermask dam still exists which would stop the solder from flowing into the holes.
Nonetheless I have given you a coupon for all the trouble but as mentioned before, we cannot guarantee that the boards will not come out the same in future orders.
I hope that is alright, and let me know how it goes,