"The government has recently decided that all illegal immigrants in Sweden will get free health care, without any paperwork."
If the vast majority of people treated are not subject to itemised accounting, the bureaucratic expense of having itemised accounting for one small group can actually be higher than just treating them for free as well.
Not for expensive operations costing 10K++ €. The administration of those payments is already set up for e.g. tourists that get sick.
Since it seems I need to explain in more details:
The problem is that potentially anyone which can get to Sweden can get expensive treatment free. This is potentially ruinous for a small country. Just the millions of poor gypsies in Romania/Bulgaria which lack good health care for poor people ("I'm from the republic of Moldova outside the EU. I am here illegally because criminals are after me") is enough to break the Swedish health care system if they use this loophole in an organized way. Or normal citizens in those countries, for that matter. We will see...
If the vast majority of people treated are not subject to itemised accounting, the bureaucratic expense of having itemised accounting for one small group can actually be higher than just treating them for free as well.