A lot of this discussion has touched on game balance or lack thereof, but its also not strictly a matter of game balance. A parallel example of this is found in the Lawbreaker powers. To 'normal' DFRPG characters (by 'normal' I mean those who, like Dresden, try to be heroic and at least pay lip-service to the Laws), the Lawbreaker powers are completely imbalanced. They cost refresh, but offer no benefit whatsoever (because the character has reason to actively avoid using the 'benefits' of the power). And yet they they might be 'required' based on character background or decisions (or mistakes) made in the course of game play -- if the character has power and has chosen to use it the wrong way, then he loses refresh with 'nothing' to show for it. Balanced? Perhaps if you're playing a dark-side character. But for Harry Dresden, for example, its a pure liability with no upside. It's flavor given mechanics, not mechanics built with balance in mind.
So I see at least part of the reason for the existence of the Pure Mortal bonus to be based in this same concept. In DFRPG, those who grasp the supernatural and make it part of themselves (or who are grasped by the supernatural and taken over by it) are changed, and that change moves them away from humanity. Such characters are not Pure Mortals any longer, even if all they got out of it was a -0 power. Very nearly but not quite Pure Mortal is not Pure Mortal in much the same way that a very nearly but not quite non-pregnant woman is in fact not non-pregnant.
And in Dresden Files, being supernatural meants being separated from humanity/mortality/free will. Which is a large part of the reason there is a 2 refresh difference between Pure Mortals and slightly ImPure Mortals. (And yes, there is a balance attempt being made, too, but its not only balance.)
So I guess my argument against characters who are "a little bit supernatural" counting a Pure Mortals is largely one of principle, rather than game balance (though again, my argument is a bit about balance, too, because supernatural aspects tend to have more potential). And it's true that 2 refresh is a big deal from a balance perspective, far more than the advantage than gained by having supernatural aspects -- I think its the big transition from +2 refresh to no bonus (and resulting balance questions)that fuels the counterargument. So perhaps it would make sense to house rule it along these lines:
(1) Modify the pure mortal template as follows:
Musts: Pure mortals must have a high concept that is in line with their nature as a non-supernatural being. Although it is possible for such a character to be derived from a supernatural bloodline, a pure mortal is unable to tap the power of that bloodline while remaining pure mortal. It is possible for pure mortals to carry latent potential; should this potential ever express itself, the character's template (and high concept) should be altered to reflect this as appropriate. Pure mortals may not take any supernatural powers. In exchange for this restriction, pure mortal characters (and only pure mortal characters) get a +2 bonus to their starting refresh. If this character ever takes a supernatural power or switches templates for any reason, this refresh bonus goes away immediately (which may be mitigated by dropping one or two mortal stunts).
(2) Add the following verbage to any template (including custom templates, but not the pure mortal template) that has a sufficiently low minimum refresh:
If a character with this template has no more than a single power costing at most -1 refresh, then the character is considered a {choose one: Minor Talent, Freshly Emerged, Rookie, etc} and gets a +1 bonus to their starting refresh. If such a character ever gains a second power or any single power costing more than -1 refresh, then this refresh bonus goes away immediately (which may be mitigated by dropping one or two mortal stunts).
I think that this house rule adequately retains the concept that supernatural power/nature/etc is the antithesis of free will (as expressed by refresh) and further smoothes out the differences between 'true' pure mortals, minor talents, and more deeply supernatural characters. It allows for characters to play weak supernatural templates and benefit from being supernatural whiel still retaining part of the pure human bonus.
Thoughts? Suggestions? Flames? Hate? Pie?