You are totally correct, but I feel like pointing out that a surprising number of games use the 4k texture nomenclature in a totally illogical way; they label it 4k because it’s meant to look good on a 4k screen, not because the texture itself is at that resolution (or any loosely related resolution).
Which is itself really annoying. But I guess less savvy crowd might not actually understand what ‘real’ 4k textures even refer to?