The point is not just that the brain halves make inferences, but that they explicitly hide that they are doing so, and seemingly (though proving this is hard) believes they are acting from knowledge rather than inferences they have no basis for.
Whether or not they're right in any given claim is besides the point, as at any point past the split that includes an element of chance and is dependent on the extent of outside interference. E.g. just talking to a person with severed brain stem from one side in sufficiently lowered voice is sufficient to provide different information to each brain half and cause them to diverge - coherence is lost pretty much from the first moment; though the extent of it can remain quite low for some types of information for quite some time.
> You could modify the source code of a distributed database so that the nodes in a cluster were no longer guaranteed to be consistent. That wouldn't show that consistency is an illusion; it would just show that you can break stuff by modifying it.
This is a poor analogy. In this case the brainstem is the replication mechanism, not computation.
Take a multi-master database and sever the replication, but let the nodes most of the time see mostly the same data. Now change the database so that it tries to infer what the results actually should be based on patterns seen in the past, so that it actively lies to you about what the basis for the query responses are (the database tells you it is derived from inserted data, but half the time it's computed based on imperfect assumptions of what the other node will have seen).
This is what is actually observed in experiments on people with severed brain stems: You know you've fed bullshit data in, yet the system responds with providing a result with a confidence it has no justification for. You can argue we can't prove that the motivation is to maintain the illusion of self, but the effect certainly is to maintain an illusion of a coherent self - or at least try to. Unlike the database, you can ask each brain half what it based it's decision on, and the deceived brain half will usually insist it made the decision based on x,y,z, even when researchers made the decision without its knowledge.
The only change is blocking communication.
Yet when one brain half tells you it made a decision and explains to you why, you can't trust a word it's saying, as it will present itself with equivalent certainty whether or not it actually made the decision, as long as it thinks some part of the collective actually did make the decision.
Think of any part of your brain as some government spokesperson who is trying to speak for the whole, and who needs to answer questions about statements they personally never made without letting slip that it's total chaos behind the scenes.