It seems to me that people who find utilitarianism intuitive do so because they understand the strong mathematical underpinnings. Sort of like how Bayesian networks determine the probability of complex events, in that Bayes theorem proves that a probability derived any other way forces a logical contradiction. Probability has to be Bayesian, even if it's hard to demonstrate why; it takes more than a few math classes.

In that sense, it's as possible for utilitarianism to be false as it is for probability theory (based on Bayesian reasoning) to be false. If you know the math, it's all true by definition, even if some people have arguments (or to be LW-sympathetic, think they do).

Utilitarianism would be false is such arguments existed. Most people try to create them by concocting scenarios in which the results obtained by utilitarian thinking lead to bad moral conclusions. But the claim of utilitarianism is that each time this happens, somebody is doing the math wrong, or else it wouldn't, by definition and maths galore, be the conclusion of utilitarianism.