I don't think anything can be proven from this link (besides for the fact that it's out of date). "W" on BA refers to a premium cabin, yet it refers to deeply discounted Biz on LY, and deeply discounted Y on CO... (just a random sampling of 3 airlines I know decently). I don't think saying "J" or "C" have technical definitions across the board would work in a court.

I do think that BA owes the pax a decent compensation package, as they were in every sense of the downgraded, (except perhaps a technical sense, which for this purpose, is the least important sense).