The purpose of moral intuition is to help you be a good ally. That's it. This is why those close by seem more morally salient - they're the ones who you can actually be an ally to. In Singer's thought experiment about the drowning child vs. the children starving in Africa, he's trying to overcome people's natural intuition to favor those close by. Utilitarianism in general is trying to overcome a lot of intuitions about who you can realistically be an ally to - treating every person as equally morally important regardless of their relation to you.

Many of the examples in the article are constructed to omit outside observers. In the real world, this is very unrealistic. Our intuitions about the importance of acting consistently reflect the risk that we'll be discovered doing something abhorrent. Reputation is important.

In fact, if we make the examples more abstract and impersonal, then it's much easier to see how utilitarianism makes sense. What if there was no actor making a choice; instead, the two possible outcomes happen by chance or natural causes. Say the healthy patient dies from a freak accident, allowing other patients to be saved. This seems like a better outcome than five people dying, all else equal. It's only the possible effect on the doctor's reputation that makes the original a moral dilemma.

Similarly, in the riot example, if the innocent person was implicated by accident, that would be a better outcome than many innocent people dying to the mob. It's only introducing the sheriff and his reputation that makes it a dilemma.