I'm trying to articulate why I didn't just go with that word in the first place. It may be that my use of ambiguous is somewhat idiomatic, but here's why I don't like it for what I'm looking for.
Let's take this other situation where person A says that they have clearly, no doubt about it, felt God's touch in their life. Person B says that it's just their imagination.
Now, if this situation were part of a story, depending on how it's written, we could easily say that it's ambiguous whether or not it really happened.
But if this were real life, I don't like the word ambiguous. I might say that we can't know for sure what really happened, but I wouldn't say that it's ambiguous.
Maybe it's because, at least in my mind, ambiguity is part of communication. Stories, songs, and diagrams can be ambiguous (as all of my examples were), but real life can't. Real life is uncertain or unknown, but not ambiguous.
Also, this word that I'm flailing around for is a noun for such "ambiguous" situations.