Not necessarily. I used to always buy genuine HP cartridges, sold by Amazon (not a third-party seller,) with official packaging, non-tampered unbroken sticker

Not necessarily. I used to always buy genuine HP cartridges, sold by Amazon (not a third-party seller,) with official packaging, non-tampered unbroken sticker on the box, and yet one day my printer reported a cartridge as "non-genuine" and absolutely refused to accept it. Maybe the chip malfunctioned. But since that day I have stopped buying genuine and I replaced them with recycled third party cartridges. A third of the cost. And they never caused this problem. A defective system caused HP to lose a customer.