What would be the correct word for considering or believing something said by people without knowing the truth behind it?
You may be able to use the expression "to take it on faith that...". This expression introduces an idea which is accepted without further verification. Merriam-Webster defines it as: to accept (something) as true without proof or evidence that it is true ~ Merriam-Webster
Consider: "He just took it on faith that I was being a responsible and didn't ask any more quesitons."