It's a single person, or small department, using some off-the-shelf tool like Excel or Access to massage data into the format necessary to integrate it with one of the various third parties that must process it in order to get full reimbursement while ensuring compliance with regulations. The problem itself demands that huge amounts of personal data are gathered together, and the way the system works generally forces it to be handled by a regular person, on their workstation.
Obviously this data needs to be shared with the payor (e.g., Medicare). The thing is that the reimbursement regulations change constantly (not just every year or something, but literally weekly in the Federal Register), and changing regulations demand different reporting procedures and formats. The constantly-changing nature means that it's not a very good candidate for automation: every hospital (and every other healthcare provider) would need to have IT staff constantly active addressing changes, or at the very least, providers of hospital ERP/records systems would need to be constantly addressing changes, and hospital IT would need to constantly be integrating software updates.
And it's not just the payor that's a problem. There are countless third parties that communicate this data. Because cases are handled as cases rather than people, when a case is transferred to another hospital, or sent out to a specialist, that must be tracked. But frequently it's not the hospital doing the checking, it's the patient himself that checks himself out and goes to another hospital. That means that hospitals are constantly downloading Medicaid records to cross-check against their own data, and negotiating with other providers to determine who gets "credit" for the cases. Since all of these third parties have their own systems, and the number of combinations of transfers between providers is astronomical, the communication of this data tends to turn into one-off projects, demanding that a human compile the data in a way that both sides agree to.
So it appears that part of the need to keep human hands in heaps of personal data, is driven by the nature of our healthcare regulation.
(I know the article is written about the UK, but I'm assuming that much of what I've said generalizes across the ocean)