That was about HP's ink subscription service, "HP Instant Ink", where your printer stops printing if you stop renewing your ink subscription and try to print with the subscription supplied cartridge.

I'm on my 4th HP Inkjet, and none of them did anything remotely similar. One worn down (which was a bottom of the barrel model), the two of them was donated, and AFAIK one is still pretty operational.

I'm regularly using my Deskjet Ink Advantage 4515, which is ~10 years old at this point.