Yes, that's exactly what is being said. You calculate the value of both types of lives, divide by the costs, and go for whichever provides the highest resulting payoff.

In other words, you have not naively assigned the same utility to every life saved, and you have calculated things in proportion to your best guess as to their actual expected utility. You shut up and multiply. This is exactly what the sentence you objected to was trying to say.

Perhaps you already grok this principle so well that you were assuming the sentence was meant to say something else? Otherwise I'm confused why you feel the need to make that point.

That's true, but the discount factor still applies. Helping people in the third world is cheap enough relative to helping people in the first world that it makes up for the reduced utility per year of life saved.

That's not where the misunderstanding lies, though. If we take the sentence:

"people in third world countries have unpleasant lives, therefore we should discount the value of donating to the charities helping them accordingly"

It is very much true, almost trivially so. The value of the donation gets reduced by a factor proportional to the unpleasantness of the life versus some other, more pleasant life in a high-prosperity region. So if saving either life costs the same, or if the difference in cost does not cover the difference in unpleasantness, then it is better to save the pleasant life with this money.

However, what seems to be the issue here is that "discount" and "accordingly" are being charged with connotation, rather than taken as mathematical factors in an equation. It is true that in the current state of the current world we live in, the E.U. of saving a life in a third-world country is better than saving a life in a first-world one, because it is much cheaper, and because it doesn't correlate that well with life-pleasantness anyway. This may be where the objections are coming from.

So what's being said is that you should calculate the expected utility of a post-apocalypse (or third-world) life as lower than that of a modern life. Then, calculate the costs as normal. Then, calculate the probabilities as normal. Then, calculate expected utility in proper fashion, having accounted for the difference in value.

It's all very much straightforward to me and implied by most utilitarian calculus I've seen, so I'm somewhat baffled by the presence of so many objections to that claim.