But none of these things are true. You are wrong about all of it.
> If we knew you murdered someone, we'd know you were a murderer.
That's a tautology. Imagine if I were accused of murder. Do you not think that you would be more inclined to give me the benefit of the doubt that I might be innocent if you knew me than if I were a stranger?
> It all we knew about you was that you were a friend of a professor that got you into your graduate program, we could not possible think much at all of you.
What if the professor told you that I was worth admitting? Would you not lend credence to their assessment?
> I choose to believe you are a rocket scientist.
Why? Because I said I worked at NASA? How do you know I'm telling you the truth? Even if I am telling you the truth, how do you know that I got my position at NASA on my merits? For the record, I did not. I got it because I knew someone. And the person I knew got their position because they knew someone.
This is not to say that I was unqualified, or that my boss was unqualified, or that we got our jobs purely because of nepotism (though that does happen as well). The situation was that JPL was actively recruiting people, and one of the department heads recruited my boss because they were grad students together at Yale, i.e. they knew each other, and my boss was my Ph.D. advisor, and so he recruited me because he knew me.
Personal connections give you access to opportunities that you would not otherwise have had (might not have even been aware existed) and the benefit of the doubt if you screw up. It's not like you can just go have a beer with a professor and get in to Stanford without doing anything else. But personal connections tilt the scales very heavily in your favor, and vice versa.