“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]
(..) Whatever happened to "the pen is mightier than the sword"? Martin, as the president of the United States... ...this comes with the full weight, power and authority of my office: Fuck you. - You okay? - Can we get down to business now? I'm gonna need you to open this for me. (..)2013 White House Down
(..) "Cale frequently does not complete his field reports on time." Nothing to do with protecting someone. "Sergeant Cale demonstrates a lack of respect for authority. Sergeant Cale has raw potential but seems determined not to realise it." You can keep reading that. That is not me anymore. (..)2013 White House Down