That is an answer, but not a particularly applicable one.
Yes, there were exclusive skins in the old days, but even then there was generally about one skin per mode (possibly up to 3 or 4 skins) where this takes a single skin and decides to exclude a single mode from the entire reward. It is similar, but simply not the same situation.
If Blizzard were to create a separate skin for LFR for completing the quest in LFR, then it might be close enough to be called the same... but it is not.