Even if the absolute number is wrong (which it isn't, necessarily), the relative trend is dramatically upward, and the biases you describe wouldn't appear to account for such a trend.
> The results show a record-high 415 children killed themselves in the year through March. That's up nearly 100 from the previous school year.
I believe this is mirrored in other countries. The pandemic really hasn't been great for a lot of middle/high school kids.
Also: please be mindful that generally if some "obvious fault" occurs to you, it probably occurs to the people for whom this is their professional area of expertise or even life's work, their work has likely been reviewed by a number of their peers, etc. Internet discussion forum commenters are highly unlikely to be the first person to think of some flaw in their work.
I'm not saying they always will do said correction, but that if you're going to be skeptical, check to see if the correction was made instead of just dismissing or discounting the data, and be especially careful about your personal biases.
Note that such corrections might only get a passing mention because corrections for under-reporting is so common in epidemology.