From the USCG website-
"The United States Coast Guard is a military, multimission, maritime service within the Department of Homeland Security and one of the nation's five armed services."
"National Defense: Defend the nation as one of the five U.S. armed services. Enhance regional stability in support of the National Security Strategy, utilizing the Coast Guard’s unique and relevant maritime capabilities."
"National Security
For more than 210 years, the Coast Guard has served the nation as one of the five armed forces. Throughout its distinguished history, the Coast Guard has enjoyed a unique relationship with the Navy.
By statute, the Coast Guard is an armed force, operating in the joint arena at any time and functioning as a specialized service under the Navy in time of war or when directed by the President. It also has command responsibilities for the U.S. Maritime Defense Zone, countering potential threats to American's coasts, ports, and inland waterways through numerous port-security, harbor-defense, and coastal-warfare operations and exercises."
As for them not engaging in offensive ops, that's BS.
Many of the landing craft in WWII were manned by the USCG. You don't get much more offensive than that.
During OIF there were two oil rigs that needed to be taken in order to take the port. A US Army (YES ARMY!) tugboat twice navigated through the minefield at night to transport boarding parties to each oil rig. One boarding party was USCG, the other USMC. Taking a key objective offensively during an amphibious operation is about as offensive as you can get (even if it was by Army tugboat
)
Plainly, the USCG is a military service
by statute, so that's pretty much all there is to that no matter what they do, or who they work for.