You are saying that it could be that spacetime was flat, and light followed a curved path.
Let me flip your question around. How could you differentiate, these two cases:
all known particles are following a bent path when they interact with the gravitational field (in your case spacetime is flat, so spacetime is flat, but particles follow bent paths), meaning that gravity does not curve spacetime itself, just curves the paths of particles
spacetime itself is bent (because gravity bends it), so everything we know, all particles must follow its curvature (since they exist in curved spacetime, they must follow it)
Experimentally, you could not tell.
We use the phrase gravity curves spacetime, and it is confusing, I understand.
You can take electromagnetism. The only reason we do not use the phrase the EM field curves spacetime, is because there are particles we know, that are not affected by it, so the EM field does not bend their paths (and because they can bend in two different directions). So the EM field cannot curve spacetime. Or in your case, the EM field curves spacetime, but some particles (EM neutral) follow a different path, not the curved path. This curvature of EM charged particles is because of the interaction between the particle and the EM field. Not because the EM field would curve spacetime.
In reality, in the case of gravity, we cannot tell. It could be either way. The most commonly accepted view is that gravity bends spacetime, and the curvature itself is the deformation of spacetime itself. All known particles (not just photons) follow this geodesic.
But this is not correct. All known particles with stress-energy will follow this geodesic. Do we know of any particles in the SM that do not have stress-energy? No. So all particles in the SM follow these geodesics.
The geodesic is simply the path followed if no external forces act on the object. It's the general relativistic equivalent of moving in a straight line.
This says too, that no forces act on the object (photon in your case) itself, but the force (of gravity) acts on the fabric of spacetime itself, curves it, and the object (photon) will just follow the geodesic.
We use experiments to justify our models. In our experiments, we can tell whether particles follow certain paths, but we cannot tell in our experiment whether the fabric of spacetime is deformed or not. The experiments only work with particles (photons in your case). The experiments tell that GR is right, and all known particles must follow these geodesics (if no external forces act on them).