I was told on the phone they had seats in Y and I could have sat there for the rest of the flight and received the fare-difference back as a refund.
Not sure if it's still standard in these cases, but once when my CW seat motor broke in the incline position not long after take off, it became difficult to use during flight, never mind impossible to sit in at landing. And the flight was jammed in CW, F and WT+.
They offered me a Y aisle seat and a "refund" for the difference. Thought oh well, inconvenient, but still have the rest like FT immigration, arrivals lounge etc. holding a CW boarding pass. And as long as a refund is in order, then it's just bad iuck.
However...found out upon applying for said "refund" that BA were using (even though I challenged it and lost) the fare that would have applied for Y had I bought the full fare ticket on the day of travel. Obviously, their highest possible Y fare to use against my original ticket purchase price I'd snagged on a good fare sale a few months prior.
Needless to say, that got me a 10 quid actual refund when compared to the original outlay WT+ plus Avios to upgrade to CW. And the Avios thereby were utterly wasted technically for that leg (Avios were not refunded nor adjusted for that leg).
So, just a thought to beware of what you think they are speaking of when they offer a "refund." BA seem to use their version of refund. At least in that instance. :-)