When boiling water without any other ingredients in it, why start from cold?
There have been plumbing systems in which the hot water was likely to have dissolved more [toxic|unsightly|unpleasant-tasting] material from the pipe walls or joints than the cold. In particular any system that uses lead-based solder, can leach minute{*}, but detectable amounts of lead into the drinking water, and the hot water is more efficient at this.

In this case that advice amounts to "use the clean water".

{*} Really minute. Like "Use this water all you life and not suffer any ill-effects" minute. But it can be detected, and who wants to chug down a glass of lead solution...