Also if you are using some sort of potting or coating that is supposed to be only on one side, the tenting prevents the coating from getting to the other side, which is sometimes unwanted (although for this purpose vias are often plugged, because tenting alone is not strong enough).
Another thing: prototype PCB services usually deal poorly with tenting. Chinese guys (itead, elecrow and such) usually get some vias right (=tented) and some not, even when specifying minimal hole size allowed. I think this is because the soldermask they are using is a thin liquid prior to curing and drips through the via or collapses when it's being cured.