> The use of "God" in that statement refers to an objective source.

Do tell.

Like I said, it means a supposed absolute truth. As there is no objective source, you can use a term for what would be an objective source, "god."

"[A] supposed absolute truth" Is that like a redundancy (absolute and truth) wrapped in a contradiction (supposed and absolute truth)?

If there is no such thing (i.e. no objective source) why would one use any term for it?

Why would one modify truth to be "god's own?" Is it a rhetorical claim to the authority/authenticity of an unseen third party?

It's a cutesy way of saying the actual truth. Language is full of such ridiculous contradictions used to express things, I wouldn't use this one but I don't see how it is particularly objectionable.