I think we're getting caught up in"right"vs. "wrong", when such a thing doesn't exist.
People shouldn't minimize the feelings of those around them or imply that their situation is trivial - it's unhelpful even if well-meaning. I don't think anybody gets to decide how stressful/upsetting the particular situation is for the mother in question, but it's irrelevant to the question of dealing politely with it. On the other hand, those who are the recipient of thoughtless but well-meaning comments also should handle these politely and graciously. In etiquette there's no such thing as "X behaviour justifies Y". Each person is responsible for their own conduct.
But what is minimizing to one person is extremely helpful perspective for another. I fall into the 'need positive-side comments' group for the most part. The comforting I personally find most helpful in an ideal world is one smallish layer of validation/sympathy/hugs, then followed by focusing on the aspects of the situation I can find happiness in.
If I'm in a tense, scary, stressful situation, I often feel I'm staring down the barrel of every horrific possible outcome. I become paralyzed by staring at my own wounds. I generally desperately need someone to say "It's okay, Aeris, it's just a flesh wound! [even if they are lying] Everything is going to be just fine! Just you wait, in just a few days, things will be back to normal!" To someone else, this might be minimizing their pain, and acting like their situation is trivial. For me, it's the thing that gets my mind out of dangerous emotional paralysis.
If someone does nothing but focus on my own pain, it can severely increase my negative mental spiral.
So, no, you can't actually say that this entire category of commentary is universally unhelpful.
I get what you're saying. I'm just wondering, though, if the "it could be a lot worse" is the best comment to open with. I mean, I know a lot of people that feel that the comment minimizes their feelings, including me (and I am not easily offended). Yes, things could be worse, but does that mean that I can't be upset? So, without knowing what the other person needs as far as comforting words, what do we default to?
I don't know anyone (not saying they don't exist) that gets on the defensive if someone says "I know this must be hard for you." or "how are you handling things?" I think those are good openers to guage where the person you are trying to comfort needs you to go. And I think it probably wouldn't take long to figure out if they want to be told all is going to be ok or that someone somewhere has it a lot worse or just want some sympathy for their particular situation without being told that someone is going through something harder.
In cases where one person is trying to comfort another, I kind of tend to give more leeway to the one that's upset. Yes, it's good advice to tell them that these commens, even if unhelpful, are well-meaning and they need to take it as such, but if I were to focus my advice anywhere it would be to those of us who are trying to comfort. And unless you know exactly what the other person wants to hear, I think that there are better openers, less likely to further upset, than "It could be worse."