Trustworthiness is not tied to money, the ability to make large sums of money, or the ability to convince others to loan you money/invest in you.

Depends on context; in some cases it absolutely is.

Courts often "trust" people to go free temporarily if they can post bail pending trial. Lenders will "trust" you with their money in the form of a loan if you can post collateral.

Yeah, but "ability to pay a court-ordered settlement" correlates pretty highly with having some cash reserves.