Yes, pretty much. A Pure mortal is someone who invests his refresh in nothing but stunts. If you are an angel cursed to live a human life, that is your backstory, and that is fine. If you retain any supernatural powers from that background, you are no pure mortal. Hell (no pun intended), even taking true faith "powers" cost you the pure mortal bonus, and they are as close to the pure mortal side of the spectrum as you can get.
And like I said above, for a 1 refresh "power" to qualify as a stunt, it is not so much important to me, what the benefits are, but where they come from. If the angel above spends 1 refresh on an improved lore, then he can either have a lore stunt, saying that in his time as an angel he learned a lot about the supernatural world, that he still carries with him. Or he says that he is still connected to the heavens, granting him knowledge beyond human comprehension. Both can give him +2 on a lore roll, but only the stunt would qualify him for the pure mortal template.
Yes, in this case, it is sort of wobbly. I see it as sort of an active passive thing. I know what I've learned over the years vs. I have access to a supernatural den of knowledge.