although he is not vanilla, from his behaviour i would see "bester" from "babylon 5" as a negative refresh mortal. also "giles" from "buffy" when he has his ripper-moments. (such as when he was killing a mortal in cold blood because he knew that buffy would not do that, and it was necessary as this mortal was housing an evil goddess
.)
I would have said it just the other way around: Buffy is the hero, it is her nature to not kill innocents, even if it would have to be done. Giles on the other hand is capable of making that choice. Or Buffy just ran out of FATE points and got a compel.
Dexter is another good example of a low-refresh-but-not-zero character. He gets compelled a lot, but he either buys off those compels or (most often) he finds a compromise. There are certainly a few times, where the "escalation rules" are used
I always understood the "less then zero refresh" thing as a way on how a character can influence a story. Positive refresh means, you can actively push the story in a new direction, zero (or below) means you are doing what the plot needs you to do (with the occasional oddball, when you get FATE via compels).
And by that logic, at least the heroes in a story have to have positive refresh. Everyone else will be tossed around as the story needs them. Another thread mentioned an Alfred character, that would be the kind of non-villain zero refresh character I have in mind. They do what they do, because they are, what they are, nothing more, nothing less, nothing surprising. These characters don't even get FATE by compels, because they will (most certainly) never get compelled.
I have not seen burn notice, but from what little you said, I think it would be a positive refresh character, simply because he is a hero (as in the story is about him). "Getting my life back" would probably be his trouble aspect, which, I assume, is compelled quite frequently.