Um... yes that is how authority works. Someone or people have put some person into that position. Authority. . .
That's not how authority works, that's how society likes to make you think it works. Some random person says "authority" and you just accept it. That's really just marketing.
Well if they are the president, Director of Security Agencies, Senators, Police Chieft, your boss you name it, they have authority whether you agree with it or not. You don't need to follow it but what they say has authority over what they have been entrusted to.
Yes, if you accept that all people have authority, everyone has some degree of authority. But to be the authority is different.
I'm an authority, your an authority, the president is an authority, etc.
For example, the police have the authority to arrest someone under US law, or Texas law in this case. They are the legal authority to arrest. They are not the legal authority to determine guilt. A Texas court has the legal authority to determine guilt. But neither the police nor the courts have any more authority to determine who actually did something than anyone else is, you, me, the media, etc.
The power to rule is a form of authority, but only authority over what they can physical coerce. Authority, in the more general sense, does not exist in that way.
Technically only the court has the authority to determine guilt, if it is a bench trial. Otherwise it would be the jury, which isn't technically part of the court. The jury is made up of your peers.