Finally, I got it working for me. I had to install Lucid-Gnome in VirtualBox, and setup the printer as described in this bug report, then copy the URI to my real machine. It turned out that those two URI use different drivers:
hpijs (doesn't work): hp:/usb/Photosmart_2570_series?serial=MY7293132V04DY hpcups (works): usb://HP/Photosmart%202570%20series?serial=MY7293132V04DY&interface=1
So it seems that this specific problem is only tied to the hpijs driver, and that it is easily solved by using the hpcups driver instead
Finally, I got it working for me. I had to install Lucid-Gnome in VirtualBox, and setup the printer as described in this bug report, then copy the URI to my real machine. It turned out that those two URI use different drivers:
hpijs (doesn't work): hp:/usb/ Photosmart_ 2570_series? serial= MY7293132V04DY Photosmart% 202570% 20series? serial= MY7293132V04DY& interface= 1
hpcups (works): usb://HP/
So it seems that this specific problem is only tied to the hpijs driver, and that it is easily solved by using the hpcups driver instead