Anything that has not been directly observed is basically a theory. However, we have enough field and chemical evidence to adequately support the conclusion that granite initially (in the far far past) started out life as a more mafic melt.
Without getting too involved in the technical aspects of igneous evolution, not all, if any, granite
directly results from fractionation of basalt. More than likely, the primitive basaltic magma (A), originating from somewhere near the mantle, fractionated to a certain point, say to magma B, which might be half way between a basaltic composition and granite. Magma B, was then recycled and that magma fractionated to form magma C. The chemistry of magma C is somewhere between B and granite. And so on, until finally granite resulted. That's how I understand it, at least.
I believe most granite formation in the last half(?) of earth's history is sourced mainly from recycled crust (it has the same chemistry). By looking at 87Sr/86Sr ratios, you can determine whether their origin is more influenced by mantle-derived (VERY deep source) melts or is continentally-derived.
No, granite cannot be created in the lab (last I heard), but we do have large layered intrusions that exhibit this fractionation process; although I don't know of any that make it all the way to granite. I've seen layered intrusions make it as far as diorite, which is has an intermediate composition between basalt and granite (though a bit closer to the granite end).
See for example the
Bushveld Igneous Complex (South Africa) and the
Skaergaard Intrusion - a Word document (Greenland).
Layered intrusions start out gabbroic (at the base) and progessively become more felsic near the top of the intrusion. These are highly complex systems and as such, theories regarding their formation are numerous and often extremely complicated. However, current theories still favor crystal fractionation.