W fares are 100% earning on UA, and I would presume BD as well. Remember all W fares are not the same. A SQ W fare is a far different beast to a BD W fare... so try to not get confused.

Why not just phone up BD and ask them to clarify? I am fairly certain you will be fine on the W fare, and I suspect it would be best to credit it to BD to get your status back (if that;s what you care about). If not, put it in the account you intend to redeem from (so the one with the most miles in it - which may well be BD). The only reason to open a KF account and deposit there is if you wanted to fly SQ again and try for an upgrade...