I think what bugs me about all of this, is that mechanically this theoretical "Innate Wizard" isn't any different from a pure mortal. They can't cast spells, they don't have permanent bonuses (or even bonuses that last a scene), and they can't do anything that a mortal couldn't (from a mechanical perspective). However because they have a thematic difference you are making things harder for them. Because they have decided to have a magic bent instead of a skilled one. If the player chooses to describe that action in one way rather than another then your response as a GM should be in the description. As long as they are using the same mechanics as everyone else you shouldn't be arbitrarily slapping them with mechanical penalties. To take the thematics out of question, this would be like having two players choose different routes to get to the same place (for example a car and a train) and yet choosing to make one character late for no reason, or having two players decide to solve a problem in two different (equally valid) ways, and giving one character a penalty for it. That really bugs me.
In this game, if you have a magic bent, that means
you have magic. And if you have magic, that means you're not a pure mortal anymore. It means you've paid refresh to have magic.
As for the example, allowing invokes like this is more like having two players choose different routes, a train and a car...and then they both arrive on time despite the 'car' character not having a car, not having the resources for or regular access to a car, and not having any points in the Drive skill.
I mean, magical power isn't something like a gun where you can be carrying one in one scene, and not in another, and just handwave that you forgot/remembered to bring it. It's something intrinsic to the character's nature and who and what they are. If you can do things that are outright impossible for a non-magic, pure mortal to do, that costs refresh.
It's not just about pure mechanics. The thematics matter.
Except here's the other thing that was bugging me last night (that I couldn't articulate). Fate points are a method for the player to manipulate the narrative. They have little to do with the character. A player with a mortal character could indeed create fire out of thin air or at a distance, by manipulating the narrative in such a way as to emulate a stroke of luck. We as human beings (characters too) can't do any of this stuff, but as players we are enabled to have candles fall over, or have something flammable sitting near the heater. I've always thought that the only difference between a wizard and a mortal in this system was justification (though I suppose the wizard is significantly more powerful, but meh). A mortal needs to come up with a reason why things happen, for a wizard "it's magic", but there's no reason why a player with a mortal character couldn't do almost anything a wizard could with sufficient creativity.
PS: Sorry for the long and rambling posts.
I'm not disagreeing that a mortal can get a mechanical advantage out of his aspects. I'm just saying that you can't say "It's magic," without paying to use the magic. As others have pointed out, an invoke still has to make sense, and part of that making sense is having it fit with the character and his powers (or lack thereof).
And don't worry about the long and rambling, I've written longer and more rambly