The claim that the CAT(0) assumption can be dropped

The preceding theorem concerns convergence of horospheres and Morse gradient rays in the setting of CAT(0) spaces. Let the relevant horofunction, horospheres, and gradient ray be as in that theorem.

CAT(0)-assumption claim. The CAT(0) assumption in the previous theorem can be dropped.

The surrounding text labels this as a false converse and gives an example showing that convergence of horospheres does not characterize horofunctions whose gradient rays are Morse. The supplied text does not establish whether this claim is intended as a conjecture or whether it has been resolved.