>> The user does nothing to suggest sponsorship or endorsement by the trademark holder.
HP would say that "compatible with HP printers" goes well beyond nominative.
Per HP documentation, HP printers are only compatible with HP-licensed ink. So anyone saying "compatible with HP" is incorrectly stating they are licensed by HP.
Try selling a cupholder, or a cup, that is "compatible with Ferrari" and you should expect lawyers. (Ferrari famously hates aftermarket parts.)