I think that both sides of this discussion are missing an interesting facet of the "Pure Mortal" refresh mechanic.
One aspect is balance: Pure Mortals get a +2 refresh boost to balance out the fact that they can't wield all sorts of kewl powerz. One side holds this rule dear and absolute, the other side argues that magical abilities that aren't strictly an advantage shouldn't count, and therefore shouldn't disqualify the character from getting the bonus.
I'd like to propose an argument that is entirely different (at least I think it is, I didn't study every page of this discussion thoroughly):
First, recall that Refresh is basically DFRPGs reflection of Free Will. That is, the lower your Refresh, the more frequently you must act in accordance with your nature (in the form of being compelled by aspects). As you acquire powers, your refresh goes down, and you are able to exercise your Free Will to a decreasing degree. In a sense, magic or supernatural abilities are a corrupting influence on your Free Will.
The ultimate example of this is, of course, the Lawbreaker Powers. As a direct result of using magic in a "bad" way, you lose Refresh/Free Will. By using magic in such a way as to break the Laws of Magic, you have corrupted your soul and reduced your future potential for exercising Free Will. But long before that point, even learning to wield magic restricted your Free Will...
Taken in this light, the Pure Mortal bonus almost acts as a "positive" version of a Lawbreaker stunt. A Pure Mortal is someone who has not made magic or the supernatural a part of who they are. This is not to say that they can't come in contact with magic -- they can still have access to the temporary powers rules on YS92, for example. They might be able to draw a magic circle now and then as Butters did, or drink a potion made by their wizard boyfriend. The supernatural hasn't become part of who they are, so they are still Pure Mortal.
But once a character takes the red pill, so to speak, that extra layer of Free Will gets stripped away. And it doesn't matter what form that takes; it could be that they have taken to carrying an Item of Power, for example, or started dreaming prophetic (but ultimately unheeded, and therefore arguably of limited value) dreams.
Bringing this back to the OP, I would say that a character that has 'inherent but minor' magical powers, even if they merely take the form of an abnormally flexible aspect, have made magic part of who they are, and therefore should have less Free Will than others. This is distinct from characters who occasionally 'borrow' powers, because they haven't made that power part of who they are. (Note that one important distinction is that a borrowed power depends on the source it is borrowed from, and can't be wielded completely at the character's own discretion. And if it gets to the point that the borrowed power is available more than occasionally, then the character should probably be spending the refresh on the power.)
Just a thought I had. As usual, YMMV.