From 'Once upon A Time in the West', Henry Fonda tells one of his dim-witted minions exactly how he feels about his trustworthiness...
"How can you trust a man who wears a belt and suspenders...he cant even trust his own pants".
Different context, different meaning:
Back when engineers were (almost) all male, saying someone was a "belt and suspenders sort of guy" meant that he took care to be very sure of things, covered all the bases, took all negative possibilities into consideration, and thus was a most trustworthy sort...