My last HP printer would not recognize the ink cartridges I loaded, and they were official HP cartridges (I only ever loaded HP cartridges). Their system for detecting non-HP ink was a little too aggressive, I guess. I now have two Canon printers, and they take 3rd party cartridges.
I liked the Canon stuff, but longterm they don't seem to last. Have had two different ones fail. Now testing an Epson (ink comes in bottles (Ecotank), not cartridges). I agree about HP's software...terrible. Brother is about the only brand I have not yet tried.