<<< Is this an issue with (1)HP printers on non HP print servers >>>
Not as such, because I am using an old HP Deskjet 840c very successfully via a Linksys PSUS4 print server.
<<< (2) all in one printers on a print server >>>
That is a possibility. I know someone with an old Office Jet T45 which actually connects via a parallel port but, in its Properties, it isn't shown as connected to LPT1, but to "DOT..." port (don't have exact details). My own HP PSC 1215 has created a "DOT4_001" port as well.
If your all-in-one is connected via USB, but shown as a special port created by the software, it may not function with the print server. Also, the print server might only support "printing" and not any additional functions - scanning, copying, faxing from the PC.
My solution for using multiple computers (Windows, Mac & Linux) with my PSC1215 was a USB switch, but I don't need more than 4 ports - click here=