Correct. And just making the trajectory to appear straight by modifying the reference grid doesn't change anything. For example, once can see even exponential curve appear in a logarithmic grid. Force is a relation between the reference frame and the object. It is possible to consider either one as straight or flat.
While the apparent straightness of a curve depends on the choice of coordinates, there's also an invariant notion defined in terms of the connection.
This affects our understanding of forces: Accelerations live in the double tangent bundle, which gets split into a horizontal and vertical part by the connection. The horizontal part is the contribution by inertia, yielding pseudo-forces (including gravity according to GR). The vertical part is due to non-inertial forces.
