“Who gave him the 'authority' to do this?” “He didn't do it 'on his own authority' [=he didn't do it on his own]; he was acting 'under the authority of' the company president.” [=the company president gave him the power to do it]
No one 'in authority' objected to the plan. = No one 'in a position of authority' objected to the plan. [=no one with official power to make important decisions objected to the plan]
This office has 'authority' over personnel matters. [=this office has the power to make decisions about personnel matters]
(..) And Saito wasn't supposed to be shot in the chest. You have got one hour, now get us something useful, please. - What's that? - Good authority. Uncle Peter. Just make them stop. - The combination. - I don't know it. - Why does Browning say you do? (..)2010 Inception
(..) I don't know any safe. COBB: That doesn't mean you don't know the combination. Tell us what it is. I don't know. We have it on good authority you do know. Yeah? Whose authority? - Five hundred dollars, this cost. EAMES: What's inside it? Cash, cards, ID. And this. (..)2010 Inception