> Russell's Teapot [doesn't] rule
    > out the possibility of a
    > supernatural entity

You're right, it doesn't. Why don't we say that what it says is -- to paraphrase the Wikipedia article I sent you -- that "without [proof] he could not expect anyone to believe".

I don't rule out the possibility of a supernatural entity. But I don't have any proof for one or even anything that suggests to me that one is likely, and therefore the simplest explanation is that there are no Gods.

    > What if there exist things which
    > cannot be proven scientifically?

Then for the most part, they're supernatural. I assume it's possible to come up with philosophical outliers or things that are (for now) considered to be impractical to measure.

    > Science is a process invented and
    > carried out by humans, who are
    > finite and fallible--therefore science
    > is as well.

Is arithmetic fallible, too?

    > But what if the logical, reasonable
    > explanation is that it is supernatural:
    > that it exists outside of our universe
    > and is therefore unbound by its laws?

This is rephrasing my original comment starting with "If you're a scientist", so I agree!

    > why do you rule out the possibility of
    > a supernatural entity

I don't. As per a previous comment: "I simply do not believe in God, and I do not feel I have any reason to believe in God"