LotR -- Book 5 - Chapter 07 - The Pyre of Denethor

[Guinevere]

A very late afterthought to this discussion on what authority Gandalf could take command in Minas Tirith:
Well, it was Denethor himself who "authorized" him, in a way!
In "the Siege of Gondor", after Faramir had been brought back wounded and unconscious and Denethor was sitting at his bed:

Men came to the door crying for the Lord of the City.
"Nay, I will not come down," he said. "I must stay beside my son. He might still speak before the end. But that is near. Follow whom you will, even the Grey Fool, though his hope has failed. Here I stay."
So it was that Gandalf took command of the defence of the City of Gondor.
Wherever he came, men's hearts would lift again, and the winged shadows pass from memory.

Why shouldn't they feel it right to follow him, if he had that rousing influence on people! Besides, he went about the City accompanied by the Prince of Dol Amroth.

I must say, I wondered too about Denethor's servants - that they would obey him so blindly, to the degree of actually helping to kill him and Faramir ! ( "Kadavergehorsam" this is called in German) Can't understand the doorwarden either, who would rather fight to the last than let Beregond- who after all was not an enemy! pass.