Doesn't the Oort cloud belong to the solar system?

No. Total mass assumed to be tiny, and it is also dispersed. Large bodies can produce a Gravitational lens effect. But they'd need to be planet-sized, at least. read more

As I understand it, they are defining "solar system" by the region of space dominated by the outflows from the sun. It has now passed the Heliopause, see Heliosphere for more details. The existence of the Oort Cloud has not been proved, though it is sensibly deduced from long-period comets. read more

The Oort Cloud is an extended shell of icy objects that exist in the outermost reaches of the solar system. It is named after astronomer Jan Oort, who first theorised its existence. read more

The outer Oort cloud is only loosely bound to the Solar System, and thus is easily affected by the gravitational pull both of passing stars and of the Milky Way itself. These forces occasionally dislodge comets from their orbits within the cloud and send them toward the inner Solar System. read more