My opinion has always been the idea that spacetime is just a spin-2 particle is crap. (EDIT: However, there are different lines of though. See https://en.wikipedia.org/wiki/Anatoly_Logunov#Relativistic_theory_of_gravitation where gravity is developed as a theory within special relativity. This goes against Einsteins conception of gravity, and indeed is a different theory from the theory of General Relativity.)
The statement assumes that gravity is analogous to electromagnetism. In QED, interactions between charges occur to virtual photon exchange. Shouldn't gravity just be the same?
No, because of the equivalence principle. Gravity is an intertial phenomenon, which led Einstein to the idea that we should describe it as curved spacetime, i.e. as a geometric effect.
When one wants to measure the mass of a black hole, one does not exchange a virtual graviton with it. Rather, one can merely orbit around it for a very large radius, so that we can use the formulas from Newtonian gravity, and then measure the time it takes to complete a circular orbit. Kepler's third law would then provide a formula for the mass. In real life, we measure geodesic deviation, via gravitational lensing, say.
There is no virtual exchange here as there is no force. One merely measures things like lengths and durations, which are purely local processes. The effect of gravity is a global one (ignoring extended systems where tidal effects play a role). By the equivalence principle, we can always find a coordinate system where the Christoffel symbols vanish (these tell you about geodesic deviation, i.e. how fast two inertial paths starting with parallel velocities close together deviate after a small period of time).
That gravity is fundamentally different to all other forces was first realised by Matvei Bronstein. Google his name for more details.
One can, however, quantise perturbations above some fixed background of spacetime. We need to assume the perturbations are weak, otherwise how could one separate background from perturbation? One can also formulate quantum field theory on top of a classical spacetime.
One cannot, however, quantise the background. I.e. we have no idea what gravity is on a microscopic level.
On the other hand, we know an electron is a combination of left and right Weyl quantum fields, which interact via the Higgs condensate.