Locally compact + two-point homogeneous => Riemannian

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?

Tits proves in [Tits, J. Sur certaines classes d'espaces homogènes de groupes de Lie, Acad. Roy. Belg. Cl. Sci. Mém. Coll. in 8$$^\circ$$ 29 (1955), no. 3, 268 pp. MR0076286], page 220, the following. If $$M$$ is a locally compact and connected metric space which is 2-point homogeneous (in your sense) then $$M$$ is isometric to euclidean space or to a rank 1 Riemannian symmetric space. I don't know any newer references. Helgason mentions in his book some related results.