A metric space $M$ is called *two-point homogeneous* if for any pair of points $(p,q)$ in $M$ any distance preserving map $f\colon\{p,q\}\to M$ can be extended to an isometry $\bar f\colon M\to M$.

The following statement seems to be an easy corollary of Gleason--Yamabe theorem:

Any two-point homogeneous locally compact length-metric space is a Riemannian manifold.

Is there a reference for this statement?