So consider the case where there is a particle and a moving telescope:
If the particle is located at position 1, and the telescope is moving horizontally as shown, the EM radiation appears to be coming from position 2, from the telescopes perspective.
Let us now think of the object 1 as being an electron, producing a static electric field. Now, the telescope will detect the electric field to indeed be at position 1, despite travelling at the horizontal velocity.
Why is there such a difference between EM and electric fields.