So, slight digression to a mathematical representation so that we can connect this up to general relativity. The equations may look intimidating, but they really aren't.
Sine Dr worm has concluded he is in an inertial system feeling no acceleration, he scribbles down his parameterized equation for acceleration:
a = d²xᵃ/dτ² = 0 where the xᵃ are just the 4 space-time coordinates with an indexed notation and τ is a parametrization of the path.
Dr Newton does the same thing to describe the apples acceleration but comes up with a different equation since he is seeing the apple from his non-inertial frame.
a' = d²x'ᵃ/dτ² = -⌈ᵃᵤᵥ(dx'ᵘ/dτ)(dx'ᵛ/dτ)
Where ⌈ᵃᵤᵥ is an attempt at the Christoffel symbol. This is just a set of numbers that depend on the relationship between Dr worms and Dr Newton's coordinate system, and if they are not zero, show the acceleration of the apple in Newton's frame.
Turns out the above equation also comes directly from Einstein's field equations for gravity where the ⌈ᵃᵤᵥ depend on how the metric of space time changes from point to point. Now we can come to the rather ambiguous conclusion that a coordinate change to a non-inertial system is equivalent to a solution for gravity at a point in terms of acceleration. Since we really made no assumptions about whether a non-gravitational force was present, we could argue that the gravitational field at a point is indistinguishable from either a real external force or a fictitious force.
However, we have one last argument to go through. We can always make a gravitational field vanish at at point by choice of coordinate system (⌈ᵃᵤᵥ all zero, aka Dr worms free fall frame). But, we cannot make a gravitational field vanish over an extended region - there is no choice of coordinate system that will do that. So, we might be able to argue it Is fictitious at a point, but we would be forced to conclude that it cannot be a fictitious force over an extended region.
-