The issue w AMZ is the sku mixing. Two or more different batches of stuff get mixed. A lot of the bad stuff are rejects or seconds that get the same packaging, so w Amz it is always a small chance.
Even without the mixing Amazon will occasionally have a "fire sale" on things sold by themselves or 3rd party stores and every time this happens the recent reviews are that the product was expired, or used, or damaged, etc. Even for products where returns aren't accepted which just adds insult to injury. So it's just dumping of worthless stock. For example this seems to be the case with air friers (only because I had my eye on this) every Prime Day, they all get flooded with dozens of reviews that the product was damaged or used.
I don't trust Amazon offers because of this. So I either just buy the super cheap, disposable stuff where a trip to a shop isn't worth it, or things that have guaranteed free returns. Sometimes I'd rather order online because I have a guaranteed window to test and return if it's not what I want. For purchases in person the law here doesn't guarantee a return window for products that work but just aren't what I thought they'd be. Or I have to argue endlessly at the store for them to take it back.
To elaborate - in NYC, I usually avoid ordering from Amazon for anything where it's cheap or something health-related, but even when I've sometimes given up finding it easily elsewhere and bought it there, it's not been, as far as I could tell, a counterfeit item.
That's not to say I can easily prove that or that I'm encouraging people to order from there, but I personally haven't encountered boxes full of things other than the intended item, or the like, and I would suspect the problem's prevalence varies heavily with volume (and thus, turnover) and location.