There is a difference between a claim being unproven - and properly erring on the side of caution and skepticism - and claiming that the story has been investigated and debunked (when, to my knowledge, it has not).

It's on him to deny it, yes. He doesn't have to prove that it's illegitimate, but if he doesn't even say so, then that's reason enough to assume it's true.

This attitude doesn't seem reasonable. Anyone can make up random nonsense about someone else (no federal libel laws in the US...). Acknowledging the nonsense will only legitimize it. Why should the subject of the nonsense have to invest time and energy in debunking/denying it?

Bubolinski, a recipient on the emails recovered from the laptop, has confirmed that those sent to him are genuine. Has that claim been debunked?

If you are simply saying that the evidence isn't strong enough to say one way or another, fine. But "roundly debunked" means, at least to me, that there has been an investigation and that the factual claims have in some way been shown to be false. That, to my knowledge, hasn't actually happened.

And sure, "anyone can make up random nonsense", but these claims aren't being made by "anyone", but by people with closeness to the situation that not just anyone can claim. And they aren't random nonsense; they are part of a pattern of explaining how a family has become fabulously rich on a 176k salary.