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Chris, Russian translaters of the 19th century referring to Josephus have got nothing to do with what Jesus said in his spoken Gospel around the year 30!
That what Josephus wrote is not in referrence to Jesus but to the Jewish Revolt of the years 66-70 AD.
This revolt brought about the destruction of the old Temple and alter, which is what Jesus prophesied.
Prophecies to this event were also made by some Old Testament prophets, particularly Zecchariah.
As for the wailing wall, no, it is not a part of the old temple (the second temple) which was built around the year 520 BC after the return of a part of the Jews from Babylonian exile, but was a wall buillt by king Herod some time in the late 1st century BC, in his projects to embellish the Temple.
King Herod's project of adding new structures to the Temple actually was still going ahead long after his death and was completed only several years before the destruction of the Temple in 70 AD.
The Jews resident in Jerusalem, around the year 630 AD, reverted to the wailing wall as a place of wailing after an Arab sultan erected the mosche in the place where the Temple had once stood, as they did not like the idea of going to said mosque to wail and lament.
These Jews erroneously believed that the wailing wall was part of the original first Temple built by king Solomon.
So no, the "no two bricks will remain one on another", as spoken by Jesus, was totally and utterly fulfilled!