Where is the Network printer connected? Is it connected to one of the laptops, or, is it connected to a hub or router on your network? I never had this problem, but, I used to make the mistake of not unchecking the "shared" option on desktops/laptops that didn't have the printer attached to them. Some of the other desktops/laptops, instead of finding the printer on the network, would attach themselves one of the other computers that had "shared" option checked. Which resulted with a printer queue from one computer looking at or adding to the printer queue of one of the other computers where the printer wasn't attached. (Is that confusing? It is to me.)

If your printer is attached to a hub or router, make sure that none of the computers have the "shared" option checked in the printer setup. If your printer is attached to another computer on the network, make sure that computer is the only one that has the "shared" option checked, and see if that helps. If you already set up the printers with the shared option checked, you might have to delete the printer and set it up from scratch on each machine, including the one which has the printer attached to it.

If that doesn't help, wait a bit, and see if anyone else has a different answer. Maybe someone who has already come across the problem of "Printer Gone Wild" (Heh). You never know, folks here have set up a lot of networks and a lot of printers in their day, and might have just seen this problem before.

Edit: Just another thought. Make sure you have the correct printer driver in the setup, or, install the hplip-gui application. I have all HP printers, and sometimes using hplip does a better job than cups.

Duplicate printer is the same as the printer having the problem, and works. Yes, I agree that is strange. If there was something going on with the printer queue on the computer, it would also have the same problem with the second printer. At this point I would check to see if both printers contain the same info in their setup. Maybe one setting is different causing the problem.
You can't really compare the windows drivers to the Linux drivers. Just their slight difference makes them apples and oranges.
I'd also look at the printer queue on the computer, just to check to see if only one job is present when sending the test page. I really don't think that's the problem, but, it's one more thing to check.
Back in the 80's I used to write custom drivers for documents that were sent to old Epson dot matrix printers, and while I realize that today's drivers are totally different, it's hard to figure why the same page keeps repeating. If it was a hardware problem, it wouldn't work correctly while attached to windows.
Sorry, I'm just thinking (typing) out loud. I guess I would compare the setting in the printers next. Maybe the problem one is looking for a different EOF code, or it's page multiple settings.

I just took a look at the pdf on your printer: http://static.highspeedbackbone.net/pdf/HP-Laserjet-4015-Series-Manual.pdf
Page 19 has a setting for the default number of copies. It couldn't be something as simple as that, could it?

Well, good luck. Maybe, like I said earlier, someone else might have another idea once they see the thread. At this point I'm just guessing.

Tom