Wait why does Admiral Kirk need permission to take the Enterprise to the Genesis planet? Isn’t he an Admiral?

I get the impression from the design of his rank insignia that he’s not a particularly important Admiral, but what’s the point of being an Admiral if you can’t just borrow some ship, any ship, (why does it need to be the Enteprise) just to pick up a corpse you accidentally left behind?

Oh Genesis is classified? Sure I get it! But he was there when it was formed! He already knows about it!