The Short Version
The claim is well-supported by peer-reviewed physics literature and high-authority institutional sources. General relativity admits spacetime geometries — such as the Alcubierre warp metric and traversable wormholes — in which effective transit between two points occurs faster than a light beam traveling the conventional path, without any local object exceeding c. The claim's careful qualifiers ("theoretically possible," "effective speed," "some interpretations of physics") precisely match how mainstream physics discussions frame these solutions, even though significant engineering and energy-condition obstacles remain.