Okay, how did the verse with the name of the god of the Christians make it through all those copies of the Bible (2000 years old) if it was a sin to "say" it?

Fascinating.

As for "thy God" not being a proper noun, you're quoting from your holy book.

Now, which god is "thy God" referencing in your holy book?

"One nation, under God"

But you don't see how the reference is the same?

"One nation, under God" uses "God" as a proper noun. The name of the god of the Christians.

It was put in there to differentiate our indoctrination oath from the indoctrination oaths of the "Godless Communists" with whom we were engaged in the "Cold War".

The chapter you quoted, and all throughout your holy book, capitalizes anything refering to the god of the Christians. "Him", "His" and so forth. This is because it is your holy book about your god. It also capitalizes "Son" when refering to God's Son, Jesus (John, 3:16).

For reference, check out how "god" is capitalized when refering to Zeus or Thor in historical texts. Here's a link to Bulfinch's.

[link|http://www.bulfinch.org/fables/bull1a.html|gods]