No, it's because the camera moves around the plane with the right speed to keep it in the same spot as the background from the camera. You can still see that the plane moves, but it's subtle.
I agree. The plane is moving, but the camera's movement and the relative speeds of the two planes makes it harder to see. If you scrub quickly through the video it's easier to see it moving forwards and downwards.
They forgot to add a shadow. Bridge casts a pretty strong shadow showing the sun almost straight up in the sky but nothing from the plane. I have seen smaller propeller planes balance out with wind speed but a jet would need quite the wind and the water is also not that stormy
The plane is also banked, it's turning.
This means as the camera moves around the plane we continue to see the plane from same angle - this adds to the illusion since it makes the plane look much further away.
To me it looks like the shadow from the bridge is a lot more vertical than would be needed to cast an airplane shadow off frame. To truly figure it out this would require tracking some points to find out where the plane actually is in relation and measuring its size against cars on the bridge. Way too much effort. Need Captain Disillusion