The same theory of semiclassical gravity that predicts Starobinsky inflation (de Sitter-like solutions driven only by higher-order curvature terms) also predicts flat space to be unstable to small perturbations. When semiclassical gravity is modified in a way suggested by and consistent with the perturbative nature of its derivation, flat space is predicted to be stable, in accord with observation, but Starobinsky inflation is no longer a solution. The modified semiclassical theory, constrained to only solutions perturbatively expandable in ℏ, has the same dynamical degrees of freedom as the clasical gravitational field, despite the presence of fourth-order derivatives in the field equations. There are no de Sitter or de Sitter-like self-consistent solutions except in the presence of a cosmological constant, so inflation generated purely by curvature is not predicted. Furthermore, linearized gravitational perturbations in a de Sitter background (with a cosmological constant) show no signs of instability from quantum effects.