1. As other commenter said, X causes Y does not mean that Y implies X. There can be another cause for the Doppler.
And surprisingly,
2. There is at least one known mechanism that cause Doppler WITHOUT moving: when the observer is in a gravity well (ex: earth) and observing a stationary object outside the gravity well (ex: some fixed point in outer space)
As I've mentioned in another post, that leads to questioning one of the most well tested theories in physics, so you need extraordinary evidence to prove it over something as elementary as doppler shift. Like, if it's Earth's gravity well causing us to see things differently, then things that are further from Earth should observe things differently.
There is already extraordinary evidence that something in physics is behaving differently at larger scales: the behavior of galaxies (spin, gravity pull) doesn't match their mass. Any mass. There is no single mass value that predicts their entire behavior correctly. Thus dark matter, dark energy etc competing theories, which are so far untestable.
It wouldn't surprise me if we discover someday another Doppler mechanism that occurs at those same large scales
> There is at least one known mechanism that cause Doppler WITHOUT moving: when the observer is in a gravity well
This is gravitational redshift, not Doppler shift. Doppler shift specifically means redshift due to an object moving away--but to really be correct that definition has to be limited to flat spacetime, or to a small enough region in a curved spacetime that the curvature can be ignored.
1. As other commenter said, X causes Y does not mean that Y implies X. There can be another cause for the Doppler.
And surprisingly, 2. There is at least one known mechanism that cause Doppler WITHOUT moving: when the observer is in a gravity well (ex: earth) and observing a stationary object outside the gravity well (ex: some fixed point in outer space)