I think she misspoke. APD tax is charged by the UK govt. on Premium cabins; upgrading with miles triggers an additional charge - even AA has to levy this for flights exUK.
There may also have been a modest offline fee for arranging the upgrade on the phone, as is the case with many airlines these days.
Here are the T&Cs, which are pretty clear:
http://www.britishairways.com/travel...deba#upgradeba
It's a shame you were disappointed, but it's still a good deal on the airfare and you can often upgrade for cash at check in or through Manage My Booking at ba.com