Earlier quoted context omitted.
Claims, yes. But he doesn't claim it. He puts it forward as a hypothesis. All useful hypothesis are, by definition, extra-ordinary.
Of course. It was the phys.org post which invoked Sagan's quote, and I was merely reusing it for rhetorical effect.
Minor nitpick, but while Sagan popularized the saying, it probably originates with Laplace's "The weight of evidence for an extraordinary claim must be proportioned to its strangeness" (which is itself a rephrasing).
This makes sense in historical context; the quote comes from 1814, two years after Laplace published the most well-known formulation of Bayes' theorem, which is exactly what the saying embodies.