Don't confuse the SM-3 with the SM-2. They both have different capabilities.
Also There is much more to an Aegis system then meets the eye. Especially in it's ability to network missile tracking data from, aircraft, satellites, ground sensors, and ship radar. It can track any missile from it's launch till it comes into range of the SM-2/3. In other words the launch could be 2000 miles away and the Aegis BMD will be able to see it and start calculating a firing solution.
Demonstrations Show Satellites Extend Range of DoD Sensor Network Technology
Demonstrations Show Satellites Extend Range of DoD Sensor Network Technology
"The Johns Hopkins University Applied Physics Laboratory (APL) in Laurel, Md., successfully concluded the last of three proof-of-concept demonstrations showing that satellites extend the U.S. Navy's Cooperative Engagement Capability system's range for anti-aircraft warfare and ballistic missile defense applications. The tests were conducted jointly by APL and Lockheed Martin Space Systems Company, Sunnyvale, Calif., under the CEC space applications project funded by the Missile Defense Agency and managed by Naval Sea Systems Command.
The APL-conceived CEC system enhances a battle group's war-fighting capability by fusing measurements from a network of ship-, aircraft- and land-based sensor systems into a highly accurate and continuous air picture available to all ships and aircraft within the group. CEC significantly extends the range of countering air and missile threats, thus providing more time to engage difficult threat aircraft and cruise missiles."