Definition 1.d. at M-W.com is "be permitted by conscience or feeling to "

Thus I re-work Cuomo's statement as:
"I also saw up close and personal the suffering that our people are facing and the devastating toll that this economy has taken. And it [is not permitted by conscience or feeling to be] underestimated."

It seems to me a common usage. Much like "Behavior x cannot be allowed".

Sometimes we use "cannot" in a quasi "moral" sense, to mean something like "should not" or "must not" or "ought not to."

And — I think it's clear, as others have stated — sometimes we use "cannot" to mean, essentially, that something's not desirable. I agree with others that "cannot underestimate" is a kind of shorthand for something like "cannot underestimate without inviting bad consequences."

Maybe we're talking at cross purposes, though. I get the feeling that maybe not everyone shares my intuition about "cannot" and so the word might effectively have a different meaning for me than for you.

I'm like boynamedsue above and not like Ellen K. For me, the sentence "Men can't treat women that way" is an utterly unremarkable way of saying "It's bad for men to treat women that way." I wouldn't interpret it as "It's impossible for men to treat women that way."

I don't think this question needs a massive investigation of modal logic. For some speakers of English "Must Not" can be replaced with "Can not" in all the former's range (though the reverse is obviously not true). This is simply a matter of usage, and after reading the older post you linked, the modal logic seems to confuse rather than clarify the issue.

If English speakers consider "must not" to be replaceable with "can not" then the sentence "The importance of logic can't be underestimated" is POSSIBLY logical. Of course, it may not be, as the speaker may understand the "can't" in his utterance to be related to possibility not to obligation.

But I reckon this "error" comes from people initially using "can't" in this way, and the expression has since spread, rather than being an inherent failure in the brain's logic circuits. The presence of the can't makes it stronger than shouldn't, and everybody understands what is meant so… well, no big problem?

Especially when we compare with Spanish frases like "hasta que no vuelvas" ("until you don't return")

[(myl) Please, everybody, if you're interested in this subject, try to learn a bit about the different kinds of modality, their complex alignment with the various ways of expressing modality in English, and the various modal logics that help keep straight how they interact with negation, with other operators, and with each other. This topic is somewhat complicated, and if you try to learn (at least some of) what a few hundred years of logicians and semanticists have figured out about it, you're likely to get confused. (I don't mean to suggest that the logicians and linguistic semanticists have it all figured out, or that observations from outsiders are never useful; but the fact is that there's a real body of knowledge here, and trying to sort out the phenomena without taking account of it is like trying to make sense of orbital mechanics purely on the basis of common sense.)]

"Can't" does not equal, "impossible to be right", for me.

"Men can't treat women that way."
=
"It is impossible for men to be right when they treat women that way."

"The role of Polish Airmen in the RAF can't be underestimated."
=
"It is impossible to be right when one underestimates the role of Polish airmen in the RAF."

This is actually a case of grammatically logical phrase being taken on as a set expression free of actual analytic content. The only poor monkey brains here belong to the linguists.

The "can't" in the common phrase "can't complain" seems similar to the "can't" in "can't be underestimated". Everyone understands it's not literally impossible to do x, it's just unwise/poor form. Is this really a confusing usage?

[(myl) If this idea interests you, please see "'Cannot underestimate' = 'must not underestimate'", 11/6/2008, linked and discussed above, where your suggestion (which has also been made by others) is considered in detail and at length.]

I know that нельзя is either "can't" or "shouldn't" based on context, but what I'm trying to ask is if you've seen similar confusion between perfective and imperfective with other verbs, or if it's just недооценить/недооценивать.

Ooh Eee, Ooh ah ah…

My explanation could be rough (or even wrong) since I'm not a linguist, just a native speaker.

Is it possible that the use of "нельзя недооценить" for "нельзя недооценивать" has something to do with speakers deciding to mark the semantics of aspect and modality differently? Or do you only see this confusion for this pair of verbs?