That's the problem though. If there are clear eligibility criteria, and a computer program lets the operator enter information and answer eligible or ineligible, that's an algorithm used to cut off care. If a computer program decides that someone is ineligible because they're not a US citizen, that's an algorithm deciding. If the computer figures out that you no longer live in the service area for your plan, that's the algorithm deciding to cut off your care.
I would expect any insurance provider to use computer programs (i.e algorithms) to decide whether someone is eligible or not. The problem is what kind of algorithm.
...and how its outputs are interpreted. Ultimately it's less about what kind of algorithm and more about how it's used, or in this case abused.
As another user mentioned, that 16.6 days should have been the mean or mode of a posterior distribution, from which you could obtain 75% and 95% credible intervals, or at least a conditional expectation accompanied by an (estimated) sampling error and traditional 75/85/95/whatever% confidence interval.
Crossing the 17-day line could have flagged this person's case for manual review. Even if the 95% credible interval was 15-18 days, anyone who understands how statistical models work would understand that manual review is a more sensible reaction than automatic cutoff, unless you simply don't care about the 5% chance of falsely denying people health coverage.
The fact that the model is statistical is not more problematic than a chain of if/else decisions. The problem is the fact that good statistical practice was disregarded in its usage. And as others have said, there was no intention of pursing good statistical practice here, and no reason to ascribe any benefit of doubt to any decision-makers involved in deploying such a model/algorithm. It's just a fig leaf for wanting to deny people health coverage.
I would expect any insurance provider to use computer programs (i.e algorithms) to decide whether someone is eligible or not. The problem is what kind of algorithm.