  Under natural conditions, the null distance introduced by Sormani and Vega
[10] is a metric space distance function on spacetime, which, in a certain
precise sense, can encode the causality of spacetime. The null distance
function requires the choice of a time function. The purpose of this note is to
observe that the causality assumptions related to such a choice in results used
to establish global encoding of causality, due to Sakovich and Sormani [9] and
to Burtscher and Garc\'ia-Heveling [2], can be weakened.
