Earlier I responded to your post on the same issue in an older thread that you added to, before I realized that it was the same issue we were discussing here.
http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=4204839&SiteID=2
On the PC that is "sharing" the network attached printer, open OneCare, click Change Settings and go to the Printer Sharing tab, uncheck the option to share printers. Also, clear the shared printers offered to the other PC(s) by going to the same tab on those PCs.
All I can think is that the HP software is installing something that makes it appear that the printer is local to your PCs and not a network printer.
If you want to report back the results after trying the above, continue it here rather than the old thread in the Install/Activate topic folder, please.
-steve