The half that's wrong is that the admonition ignores a vital
possibility: the gauges may show way LESS fuel than you expect. (Say
you're supposed to have 3/4 of a tank left, but the gauge shows 1/8.)
In that case (if the gauges are working well enough to meet the
airworthiness requirements) you know you've got a problem--perhaps a
fuel leak, which your consumption calculations can't warn you about
without the gauges. A leak may be a very infrequent event, but
aviation safety is about being prepared for unlikely problems, rather
than unnecessarily relying on the gamble that it will never happen to
you.

Very good point.

A fuel guage rapidly dropping toward E would cause me to go for the
closest airport (hopefully with gas -- but I wouldn't insist on that!).