Depending on what she means by "a few weeks old" - I couldn't leave either of mine to cry/shout, because they both had a hernia (not an adult style hernia, it's where the tube down which the testicle travels from the abdomen to the scrotum doesn't close off at the top end like it's supposed to, so any pressure in the abdomen (like from crying/screaming) can force a section of the large bowel down there too. This is mostly reducible, but if it carries on, you run the risk of strangulating the bowel, leading to all sorts of problems.
So no, I didn't leave them to cry prior to their ops, at ~7wo.
At around 3mo, they both developed this issue with crying where they couldn't always catch their breath - they'd cry out, but be unable to breathe in again. Scary! So I didn't leave them to cry then either.
By the time Ds1 was in the cot, at 6mo, he was also able to pull himself up on the side of it. I tried getting him to "self settle" - leaving him to cry while sitting in my own room listening to make sure he was catching his breath - and then going in to check he'd fallen asleep when he stopped whimpering. Twice I found him asleep, head over the edge of the cot - he'd fallen asleep while standing. I stopped that as well after the second time, just wasn't worth the risk that he'd suffocate himself.
I realise my experience is just that, MY experience (Ditto with my comment that swaddling sucks - it did for me and my babies - and I should have been more explicit in my first mention of it) - but as many others have pointed out, it shows that the prescriptive method given on both the MN page and the paper article is NOT going to work in every case. By all means, have a SUGGESTION page that SUGGESTS these things might work; but add a large caveat that they MIGHT NOT EITHER and that this is down to the baby, not the mother's failure.