“How is the investigation of US president trump by the US congress an independent investigation…?”

Now, it is entirely fair to argue that that the powers in question are colluding in some way. But most states that haven't been subverted into authoritarianism have multiple actors with the power and (sometimes) will to investigate other ones.

I mean, if you take that argument far enough, no human could judge any other human, because none of them are "independent".