NOT trusts me about as far as she can throw me = она совершенно мне не доверяет
https://dictionary.cambridge.org/us/dictionary/english/i-wouldn-t-trust-as-far-as-i-could-throw

А вот без NOT не знаю. По логике должно означать обратное

You can only throw a person a few inches if you’re lucky. So you can trust someone that much, or not even that much. 

Also, here it says ABOUT as far…

You can only throw a person a few inches if you’re lucky.

It depends on the person's weight))

Ну тогда, наверное, "(всё-таки) (хоть) чуть-чуть доверяет"