The pre-building Finsler isometric-embedding conjecture

Assume the hypotheses of the paper's pre-building construction: there are no BPS states, $B^{\rm pre}_{\phi}$ is the resulting pre-building, and $h:X\rightarrow B$ is a $\phi$-harmonic map to a building. Let $f:B^{\rm pre}_{\phi}\rightarrow B$ be the factorization of $h$ through the pre-building. The Finsler distance on an apartment is the distance used in the paper's $SL_3$ model.

Pre-building Finsler isometric-embedding conjecture. The factorization $f:B^{\rm pre}_{\phi}\rightarrow B$ is an isometric embedding for the Finsler distance.

This would establish the claimed universal geometric property of the pre-building and determine the metric data seen by harmonic maps. The source gives no resolution of the claim.