It doesn’t do a bad job of cashing out a fairly strong corollary of utilitarianism which is generally taken to be characteristic of any utilitarian theory worth its salt viz. since each of us is only one person, and the utilitarian calculus calls for us to maximise happiness (or similar), then insofar as each of us only bears moral weight equal to one (presumably equal sized) fraction of that whole, therefore our obligations to others (insofar as the happiness of others obliges us) swamp our own personal preferences. Furthermore, insofar as (without even being a negative utilitarian) suffering is very bad, the alleviation of suffering is a particularly powerful such obligation when our responsibilities to each individual sufferer are counted up.

This is generally taken to be sufficiently characteristic of utilitarianism that objections against utilitarianism frequently cite this “demandingness” as an implausible consequence of any moral theory worth having.

So in isolation it makes some sense as shorthand for a profound consequence of utilitarianism the theory which utilitarians themselves frequently stand up as a major advantage of their position, even as opponents of utilitarianism also stand it up for being “too good” and not a practical theory of action.

In reality it’s a poor description of utilitarian beliefs, as you say, because the theory is not the person, and utilitarians are, on average, slightly more petty and dishonest than the average person who just gives away something to Oxfam here and there.