The servo has electronics inside it, including an electric engine. These will emit radiation that the plastic servo case can not dampen out. With the antenna being very close to the servo it will pick this up....

The same goes with the current through servo wires, these also emit radiation when there is a change in the current, i.e. they act like transmitting antennas.

If you're really unlucky you could in principle get a feedback circuit, i.e. moving the servo and gives noise in the antenna giving more motion and so on...