Perhaps that title should read "How much is fact, and how much is fiction" - but that's not very snappy, and I was hoping to grab someone's attention with the title alone.
I'm aware this is quite possibly a question for anthropologists or archaeologists, but I have been reading up on prehistory and the discussions around PIE caught my eye.
There are claims of a distinct PIE culture, including worship of a sky father, patriarchal tripartite-aspected societies, and so on. How much of this is verifiably true?
What exactly do you have in mind with the phrase verifiably true? Obviously, there were no written records kept by speakers of various stages of PIE; if there were such things, we wouldn't talk about records of PIE but of some named language.
While it's true that our reconstructions don't and can't correspond exactly to the practices (linguistic and otherwise) of speakers of the language(s) ancestral to modern IE languages, they're quite good. See here for a bit about the reliability of the comparative method.
Really, though, before I write anything more, I'd like to know what you mean by verifiably true.