Fact or fiction?

This is a question I have to keep reminding myself when I read Dan Brown's books. The Da Vinci Code, Angels and Demons and The Lost Symbol all raise issues which I tend to take at face value and I probably shouldn't.
For instance, Angels and Demons suggests that Galileo Galilei was part of the Illuminati - an anti-church brotherhood who stood up for science. Their emblem is said to be an ambigram (it is identical whichever way you turn it) and this was because of Galilei's love for symmetry.
To me, this makes a lot of logical sense, but in googling it, it shows that Galilei was born about a century too soon for this to be possible.

However, they were right in saying that George Washington was a Freemason.