You are either falling for the blurb in a way that BA would hope you do, or BA have changed the rules again.

If you don't travel on the ticket, there are no taxes to be paid. As such, although you may not be able to get a refund on the ticket itself, you should be able to get a refund on the taxes. You used to be able to get a refund on the fuel charges, until BA decided that actually, although not part of the ticket price, they were part of the ticket price

So don't automatically assume that because a ticket is non-refundable, you'll get no money back. Since the taxes are not inconsiderable, it does mean you'll get some money back. Of course, if you don't apply for the refund, BA get to pocket it...

The one caveat to this is that some airlines charge a 'handling fee' greater than the cost of the taxes. I'm not aware of BA doing this - but given they have decided that you have to pay a fuel surcharge for a flight you didn't take, then I really wouldn't be surprised if they'd gone all LCC on this too.