But I could argue that central agency validation _is_ probabilistic, because there is a probability that the central agency can collapse, be overtaken, go rouge

But I could argue that central agency validation _is_ probabilistic, because there is a probability that the central agency can collapse, be overtaken, go rouge, etc. And that that actually might be more probable than the blockchain 51% attack or split or whatever. I don't know what the actual math here is, I think that the essential difference is that in case of proof-of-work such a probability is computable relatively easily, while we don't know how to measure the trustworthy-ness of a third party reliably (it depends on laws, military strength, level of corruption, etc, lots of variables)