What is the deal with...

[KageTokage]

The only legitimate situations I can think of this happening in are:

1: They were standing in a SGE LB, which works like other beneficial field effects in that it lingers briefly after you step out of it. Therefore, if you try to LB someone immediately after it disappears there's still a chance they won't take any damage unless you have the Lype debuff from running into the circle yourself.

2. They're being covered by a PLD.

If there's neither of the jobs in the game, then I'm inclined to think there's some manner of hack/exploit involved.

I'd try taking note of their status bar to see if there's anything there that doesn't belong, since as far as I'm aware, there shouldn't be any way for them to take no damage without being able to see what the cause is. They've previously had silly exploits with people smuggling invincibility buffs out of other instances, so it wouldn't surprise me if something slipped through the cracks again.