general relativity - Is there a fundamental reason why gravitational mass is the same as inertial mass?

The principle of equivalence - that, locally, you can't distinguish between a uniform gravitational field and a non-inertial frame accelerating in the sense opposite to the gravitational field - is dependent on the equality of gravitational and inertial mass. Is there any deeper reason for why this equality of "charge corresponding to gravitation" (that is, the gravitational mass) and the inertial mass (that, in Newtonian mechanics, enters the equation $F=ma$) should hold? While it has been observed to be true to a very high precision, is there any theoretical backing or justification for this? You could, for example (I wonder what physics would look like then, though), have the "charge corresponding to electromagnetic theory" equal to the the inertial mass, but that isn't seen to be the case.