The link you provided states that the bad packets are detected around 1 per minute while the printer is turned on. However, we do not know the HP printer model which that user has installed on thier network. If we did know the model or at very least the print driver that is installed then perhaps we could draw some conclusions.
From what has been posted it sounds to me like some kind of heartbeat network communication triggered by the firmware of the printer is causing the problem. I'd assume something on the printer is chronologically checking in with the network equipment to let it know the printer is active or to poll the network for status updates. Also, you have not mentioned any issues with your printer applications or systems which leads me to believe these bad packets are not related to the print driver or scanning functions of the printer.
You mentioned your security logs are missing information on the bad packets. This will make it difficuly for anyone to develope a solution for you. I'd suggest installing a packet sniffer/monitor like wireshark at one of your computers and see if you can detect anything else about the problem. Gather up all the information you have collected and report it to HP. HP most likely will not have access to your specific application which is why doing a little legwork with WireShark before hand will be helpful. That way HP will be able to recreate the bad network traffic and be more likely to develop a firmware update.
Keep us posted.