I expect he used that quote to show that the existence of a Jewish village at Nazareth was doubted many years ago and is not just a new suspicion. If you doubt that quote, then you probably do not believe any of the alleged quotes from hundreds or thousands of years ago that are found in the bible from characters for whom there is NO evidence they actually existed.
Apples and oranges. Either way though, it is foolish to use outdated scholarship in order to try to prove a point. The author of the site you posted does so on a number of places. And his first quote, right at the top of the page, is one that is very outdated.
More so, when speaking about Jesus, we have more than enough evidence. As I have said over and over again, Josephus should be more than enough evidence.
The "synagogue" he was referring to was the one that supposedly existed according to Luke 4:16 "And he came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day, and stood up for to read".
Please read what I actually said. It would help a lot.
But let's examine that verse. It doesn't say that there was a specific building that was a synagogue. It doesn't say that the synagogue stood as it's own building. No. It simply states that Jesus went to the synagogue. And as I have explained, many times, in the first century, the synagogue was not a specific building, as our modern day synagogues are, but was situated in a regular home. Archeologically, it is pretty much impossible to differentiate a house from a house that is also used as a synagogue.
That is why the author of your site is not credible. He is arguing from ignorance.
As I have mentioned to you before, I tried reading your long, long, long post, but I kept seeing all kinds of silliness where you would take some facts, combine them together, and then come up with a conclusion that the facts supposedly supported your conclusions, when the conclusions you were supposedly reaching were not supported by the facts. It was obvious that you had already reached your conclusions before you began, and all you were doing was trying to collecting some facts that an ignorant person might believe supposedly supported your conclusions.
Come on, that is nothing more than a lame cop out. If my points are silliness, and my conclusions not supported, point it out. You don't have to point them all out. But stop dodging the subject, and making lame little excuses, and put up for once.
As it stands, all that it looks like is that you are making excuse after excuse on why you can't offer even a partial rebuttal to my argument. Why? Because, I think it is obvious, you know you can't.