It really is. There's no actual consistency to the distinction and the historical precedent for the distinction is based on just ignoring all sorts of dragons to claim one location is the only correct form of classification.
It's actually very rare to have any sort of true distinction in fantasy. In D&D Wyverns are classified as dragons, lore'd as part of the dragon family,called "lesser" or "bestial" dragons, and speak draconic. In MTG they are part of "drakes", a branched evolution from elder dragons considered a separate group of "lesser" dragon-like-things. Elder Scrolls makes no distinction. Wow makes no distinction (hence why this whole claim is dumb) because Wyverns are a totally separate animal unrelated to dragons, and we see here with dragon riding that not having four legs doesn't make you not a dragon.
It's made up. Just a really stupid "well akshully" claim that isn't even correct, because there's no actual consistency and what a wyvern or dragon is, is totally dependent on the individual IP or culture.