on the basis of the idea that the original debt holder has written off the charge on their taxes already and thus discharged (my) obligation to pay.
This is 100% false, and horrible advice.
Most people that don't understand this sort of thing think once a debt is charged off they no longer have to pay. It's ignorance, and incorrect.
A charge off is an internal accounting mechanism a company uses. It has no bearing on your legal obligation to pay the debt, or a report on your credit report. If the company sells the debt to someone else (like a debt collector), they get to write off the difference (if they sold a $1,000 debt for $300, they get a tax credit for the $700 difference, if they previously reported the $1,000 in income). But that has nothing to do with you. If a company elects to take the whole debt as a loss, they can claim it all on their taxes as a cancelation of indebtedness. When they do that, they send you a 1099-C and you pay taxes on the canceled debt. At that point, you no longer owe the debt (but you now owe the taxes). What does that have to do with your credit report? Nothing. Not a single thing.
Your credit report is a history of your payments. If you didn't pay the debt, and they reported it, what happened to the debt afterwords is immaterial.
In reality, despite what others think, credit reporting is still the "wild wild west." Companies report whatever they want, mostly correct but sometimes not, and the bureaus don't care. They get paid by these companies to post information, so they post it. Correct or otherwise. To "solve" the problem of potentially false reporting, you have the right to dispute a or a report. To do so, you write to the bureau challenging the debt or report. Once the bureau receives a dispute, they reach out to the company that made the initial report. If they can verify the report, they don't change anything. If they can't verify it (or just don't) the disputed "charge" is taken off your report. When you're talking about a few thousand dollars, sometimes it isn't worth the company's time to respond to a challenge (as they won't be getting paid on the debt either way, who really cares?). So many things "fall through the cracks" and you get people like that message you posted where they've gotten rid of "thousands of dollars of debt." Is it right? Nope. Not even close. But they get away with it sometimes anyway.
There really isn't a penalty for disputing a debt that you know you owe. So when in doubt, dispute it. Maybe you get lucky and it goes away. Maybe you don't and you're in the same position you are now. But don't mistake the possibility of it being removed with the RIGHT that it has to be removed.