To Atheists: Why must personal knowledge of God be inferential?

Implicit in almost all debates on this subreddit is the belief that knowledge of God must be inferential.

inference:

a. The act or process of deriving logical conclusions from premises known or assumed to be true.

b. The act of reasoning from factual knowledge or evidence.

c. Something inferred.

However, lots of our knowledge about the world and ourselves is non-inferential. For example, we have knowledge drawn directly from memory. You remember what you did on your last holiday vacation by memory, not from any process of inference, gathering evidence, looking for clues, finding witnesses, etc. Likewise, knowledge drawn from sense experience – I see a tree. My computer screen is bright. That motorcycle is loud, – is not by inference. Imagine you have a headache. How do you know you have a headache? It's direct experience; the headache is just there.

Why must personal knowledge of God be inferential rather than direct?

EDIT: So far, the responses are that knowledge must be demonstrable. In other words, unless the claim is verifiable by third parties, it is not rational. True?