Call me clairvoyant, but I think I know exactly how this altercation started.
'I'm not going down those stairs again,' growled Snaga, 'be you captain or no. Nar! Keep your hands off your knife, or I'll put an arrow in your guts. You won't be a captain long when They hear about all these goings-on. I've fought for the Tower against those stinking Morgul-rats, but a nice mess you two precious captains have made of things, fighting over the swag.' 'That's enough from you,' snarled Shagrat. 'I had my orders: It was Gorbag started it, trying to pinch that pretty shirt.' 'Well, you put his back up, being so high and mighty. And he had more sense than you anyway. He told you more than once that the most dangerous of these spies was still loose, and you wouldn't listen...'--Tolkien, Return of the King, chapter 11