If access to a warranty is what qualifies something as counterfeit, then almost everything we buy is counterfeit!
To be eligible for warranty claims, one frequently must register the product in advance and provide proof that it was purchased from an authorized retailer. There are a variety of other conditions that disqualify products for warranty coverage, so much so that it's practically always a crap shoot whether a given manufacturer will process the warranty claim or reject it with a flimsy justification.
Second-hand purchases are also generally not respected for warranty claims, but we don't consider everything sold used counterfeit.
If you anticipate utilizing warranty coverage, you have to cross all the is and dot all the ts. That's a class of consumer that isn't just going to buy from a third-party seller on Amazon without making sure that they're authorized and legitimate.
I'll also take this opportunity to note that this entire tangent arose out of a parenthetical statement where I indicated that I know someone who was selling what I consider to be non-counterfeit items from factory overruns. Nitpicks over the definition are not really related to the claim I was originally making. The anecdote remains valuable in its original context, which is that Amazon is policing FBA sellers more and more aggressively. Didn't mean to trigger a long subthread about the precise definition of "counterfeit" and whether or not a product has to be eligible for warranty to be authentic. ;)