Better link to the Josephus passage

The remark is a reference to the events of Xerxes' invasion of Greece in 480-479 BC. The Greeks first resolved to meet the Persians at the pass of Tempe in Thessaly, but they were soon told that the pass could be turned, and withdrew. They then decided to resist the invaders at Thermopylae, but that pass, too, could be turned - as the Greeks found out to their cost. With no more natural defences to protect Athens, and encouraged by an oracle to put their trust in an impregnable "wooden wall" (the fleet), the Athenians decided to abandon their city and evacuate the people to the island of Salamis and to the town of Troizen across the Saronic Gulf. The Persians then captured Athens and the surrounding lands.

When they took the town it was deserted, but in the sacred precinct they found a few Athenians, stewards of the sacred precinct, and poor people, who defended themselves against the assault by fencing the acropolis with doors and logs. They had not withdrawn to Salamis not only because of poverty but also because they thought they had discovered the meaning of the oracle the Pythia had given, namely that the wooden wall would be impregnable. They believed that according to the oracle this, not the ships, was the refuge.

-- Herodotus 8.51.2

Josephus is wrong, though, to claim that the Athenians themselves set fire to their city. Herodotus does not report them destroying anything of their own accord. He is very specific about who did the burning:

An Athenian came with the message that the barbarians had reached Attica and were destroying all of it by fire. The army with Xerxes had made its way through Boeotia and burnt the city of the Thespians (...) and Plataea likewise. Now the army had come to Athens and was devastating everything there.

-- Hdt. 8.50

And again, once Xerxes' men had dislodged the desperate Athenians defending the Acropolis:

When they had levelled everything, they plundered the sacred precinct and set fire to the entire acropolis.

-- Hdt. 8.53.2

The sacrifice of the Athenians was celebrated throughout antiquity. Since they pretty much knew what to expect from the Persians, they did kind of give up the city to be burned, which Josephus perhaps regarded as being effectively the same as setting fire to it with their own hands. However, for the Greeks, the fact that the Persians did the burning was crucial. Every burned temple was a further sacrilege; it made the gods themselves into allies of the Greeks. After Xerxes was defeated, the Greeks agreed not to rebuild any of the temples the Persians had burned, to remind themselves constantly of the atrocities the invaders had committed. Such symbolic acts would have been a bit less meaningful if the Athenians had done the burning themselves.