not defending hp at all, but it's a sub service and not any different than the cable company shutting off your internet (think: ink) for not paying. the modem (think: printer) is still there, but doesn't 'work' until the bill is squared-away, even if it's your modem-not theirs......
printer is enrolled in "instant ink". those instant ink cartridges they send out are custom, ultra-high capacity ones you can't buy retail (decreases costs of shipping by greatly reducing the frequency of those shipments). of course they're gonna shut it down if you fail to respond to the barrage of emails and popups that preceded that point.