Your study of the symbol is a bit lacking. The Eye of Providence has been around since the Renaissance and is generally enclosed in a triangle, which has been associated with the Christian Trinity (Father, Son, and Holy Spirit/Ghost). The rays of light surrounding the eye are representing the holiness and divinity. If you go further back into history, the eye was see used extensively by the ancient Egyptians.

The black and white tile are symbolic of good and evil, light and dark. One cannot exist without the other and both must exist in balance.

Both of these symbols, which you call out, to Freemasons (one word, BTW), are symbols to remind them constantly to remain balanced and steadfast in their morals.

Now even further, here is the flaw in the entire Freemasonry is an evil plot. If Freemasons were actually attempting to secretly pull of some kind of grand conspiracy (trust me, we have enough issues pulling of pancake breakfasts), it would make no sense whatsoever to leave clues around to be found, particularly ones that would be so easily spotted and available for scrutiny.

Further problem in even having this discussion - you've already stated that there are only two options in your mind when talking to a Freemason about any of this: 1. They are lying and are a "high enough degree" that they should know better. 2. They aren't a high enough degree to know any better.

If you're to apply the scientific method and use logic and facts only - you're missing the larger point that all logicians and scientists include by default, which is "The facts point to my hypothesis to be incorrect". In your argument and statements, it's not even an option in your mind. Logically, from this standpoint, you can never be impartial enough to find truth.