“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]
(..) in a place like this. Sooner or later, he'll get somebody hurt or worse. Stick with it, Paul. It may not be much longer. I have it on good authority that Percy has an application in at Briar Ridge. Briar Ridge? The mental hospital. Administration job. Better pay. Hmm. (..)1999 The Green Mile