The exact thresholds aren't known, but they're pretty low: https://www.awesomedynamic.com/amazon-prime-wardrobe/ mentions thresholds of 30 PPM (and 500 PPM for just Materially Different Complaint Rate) to get into some seller program. Presumably the threshold rate for suspension is an order of magnitude or so higher than that. 500 PPM would be one complaint every 2,000 orders.

A facetious/serious question: If "Sold by Amazon" had too high a rate of reported counterfeits, could it be kicked off the Amazon platform?

But seriously, my point is that "Sold by Amazon" should have a counterfeit rate of near zero. I'm willing to help QC third-party sellers. But "Sold by Amazon" should do its own QC. Just as "Sold by Walmart" does (for now).

Sold by Amazon probably does have a very low rate. They're many times bigger than any third party seller, so the absolute number of counterfeits is probably higher.