Phlegon

Essentially all correct, and worth setting out cleanly because the underlying texts are a mess of quotations-within-quotations.

What Phlegon appears to have recorded (via Eusebius's quotation, the best-attested fragment): in the 202nd Olympiad (32/33 CE), a great eclipse of the sun, "night at the sixth hour of the day," stars visible, and an earthquake in Bithynia toppling much of Nicaea. Astronomers have long matched this to the solar eclipse of 24 November 29 CE, whose path crossed Bithynia – a real, natural, datable event in north-west Asia Minor. No Jesus☦, no Judaea, no full moon, no three hours. The connection to the crucifixion was made for Phlegon by Christian writers wanting pagan confirmation of the Gospel darkness – and the site is right that the connective tissue ("it is clear that this is the one") shows the marks of scribal addition rather than Africanus's own argument, since Africanus had just finished objecting that a natural eclipse at Passover is impossible.

Origen's testimony deserves the emphasis the page gives it: he cites Phlegon three times (Contra Celsum 2.14, 2.33, 2.59), claims Phlegon granted Jesus foreknowledge "though confusing things about Peter☦ with things about Jesus," and – decisively – concedes that Phlegon did not say the eclipse fell at full moon. When your own third-century apologist admits the pagan chronicle doesn't match the Gospel event, the exhibit is closed. Modern scholarship treats the Phlegon fragments accordingly: as evidence for a Bithynian eclipse-and-earthquake report, not for anything in Judaea. (Whether Phlegon's original mentioned Jesus at all is doubtful; if his lost Olympiads said anything, it was likely secondhand from Christian claims a century after the fact – worthless either way, as Origen's "confusing Peter with Jesus" itself suggests.)

So: conceded, with the same closing observation as Thallus. The Gospel darkness is a theological motif (Amos 8:9 patterning), not an astronomical report; no critical case for the historicity of Jesus cites Phlegon; and striking him from the record subtracts nothing from Paul☦, Josephus, Tacitus, or the gospel traditions. A bad apologetic argument has been correctly retired – by critical scholarship first, and by this page second.