Actually it moves, not a massive amount, but it moves. To be more exact, the camera rotates (the displacement would be small in the vertical direction), which means that at speed it is pointing more upwards:
The two halves are clipped from the same video window, about 40 seconds apart, just mirrored and aligned by the edges of the video area.
It is easier to see using a magnifier tool, but it can be noticed also in the standard window. Go to the beginning (7 minutes mark), place your mouse pointer somewhere of interest, leave it there, and see that parts of the car change position (or not) with speed. The roll hoop camera housing moves by about 4 pixels with the default 360p video resolution. The top of the sidepod turning vane is also a good target, it moves a bit less, see below.
The nose camera rotates most at high speed and less at low speed or when the car is braking, consistent with a drag induced pendulum movement.
It is a small movement, but real and consistent.
E pur si muove.
Edit: The larger movement of the roll hoop camera compared to the sidepod vane cannot be explained by the different distances as I first said; the linear movement is less, but the angular movement should be the same. A model where the nose camera rotates by about 2 degrees and dives down 1-2 cm seems to more or less match (the diving of the nose opposes the effect of the rotation seen in the video, moving objects upwards, so that might make the rotation 3 degrees). Anyone with a HR video version willing to do proper triangulations?
Rivals, not enemies.