I read it already. The Marines asked specifically for the Black Watch, there were other troops available. They also asked for a specific Army unit - the same unit also. This is unusual, but not unheard of. McCain was and is full of himself. The ability to mount the op was in no way limited by available troops. You have to understand Fallujah in relation to Hue City where the Marines were the defender, not the attacker. The Marines know their history. They knew it was going to be nasty, and asked for the the best to go in with them.
Not having read the book yet and relying on memory, I believe that the Army unit was the 2nd of the 7th Cav.
Also, for those who want another perspective of the April assault, Robert Kaplan concludes his excellent Imperial Grunts with his on the spot report while with the 1st of the 5th during that assault.
"The Marines asked specifically for the Black Watch, there were other troops available."
Wouldn't this operation have been planned at the level of CentCom or General Casey? They would have determined the order of battle, not the Marines.
The Black Watch was deployed south of Baghdad, not anywhere near Fallujah. It replaced a Marine unit sent to Fallujah.