You can't prove a negative (parody)

[Mystic]

But if it is properly basic, why would it be denied (by sane people)?

Perhaps different motives, factors, reasons. You've seen people here deny free-will existing. I don't know the reason, but, it can be similar to how we leave belief in a certain moral or do cognitive dissonance. For example, a moral and existential nihilist may have so much pride as to who he is, but at the same time, deny there is such thing as objective praise or value. This would be having two contradicting beliefs.

Furthermore, if someone denied the physical universe existing or said he doesn't believe it exists, they are allowed to wonder "Well why the heck do you believe that?".

It sounds unusual, but there is nothing to be gained from denying the existence of the universe. Would we not still act in the same way regardless? What evidence is there that the universe doesn't exist? (And if it does not, how are we capable
of thought?)

Maybe we can have more control over ourselves, if we believe we are solely spiritual. We can derive more will power with this belief and hence a person like people believe in magic or spiritual dragons or Djinn, or whatever, will come to believe in it.

Some counter-intuitive things are true, but there still doesn't appear to be any reason to doubt the existence of the universe.

Exactly. It doesn't appear to you. Which is why you might ask the person who has this view to explain himself.

So which one do you find more rational?The one who says "the burden of proof is on you, I can't prove a negative, it's your job to prove a positive"?

Mario can't actually think, so he couldn't even ponder these questions in the first place.

Missing the point of the analogy again. But I will play. Perhaps your body can't think, and it's just an avatar like mario in the game simulation.