“Trust” and “Trusted Trust” are two key notions that come to mind.

“Trust” for me means formal, documented agreement between two or more parties about what they intend to being trusting about as well as the trust itself. This implies a knowledgeable or skillful disclosure. It requires a scope and an acceptance of how one party relies upon another. It is a statement about what is being exchanged and the agreement itself can be validated as factual by virtue of the agreement recorded. If such an agreement cannot be documented, a trustworthy (aka quality) trust may not be possible. Key here is that such statements can be validated by external observers not affiliated with the trust.

One party might want to promise more and be unable to authenticate or validate their part of the trust to the extent they intend to and that I would call an untrustworthy trust. One party may be willing to receive even something like that notion of risk in a trust (if the trust pertains to risk exchange) and be unable to do so, e.g. accepting a risk realized puts the accepting entity out of business. Regardless of each party’s assent, the trust was still unreliable as it was not fully factual in the statements of exchange being made. Unbounded statements are difficult in the context of establishing trust.

I’d also say there are unilateral trusts where a receiving party trusts the other party without assent. Can I rely on data from a 3rd party site responsibly if they make no statement of intent for that data to be reliable?

Without a valid trust there can be no valid relationship between risk, acceptance or transfer of risk. If a trust cannot be documented in a structured manner it cannot be used to measure risk.

From the above, I think you can begin to get at what untrustworthy is.

A nice potential side-effect of such terms might be definitive guidance for business decision-makers independent of a specific instance, aka, Best Practice guidance.

(first shot over the bow… prepare the boarding party)