I hear that used sometimes and I think it's better than trust, but it still holds some connotations that seem undesirable for the purpose: right now, a significant number of people in the USA seem to dogmatically believe that the government "can never be trusted"; these same people, if asked how much credibility the US government has, would say "none"! Etc... basically, there are lots of people that see "government" as pure evil and they make their decisions and form their beliefs around that. IMO it'd be really nice to change that, of course; but as long as people have extremely emotional responses like that, it might also be worth looking for ways that word choices can be made in order to make communication more accurate.
Frankly I don't see this as a problem with accuracy of terminology. Both trust and credibility are perfectly adequate and sufficient terms. The fact that money has any stability at all is testament to the fact that a majority of the people who use it do 'trust' the 'credibility' of the government to manage it, whether a bunch of wingnuts think they ought to, or like the terminology used to describe it, or not.