I think you really don't get it. It is not a matter of it being unlikely. It's a matter of there not being anything that can be called "stopped" except relative to something with the same velocity.
On earth, we say we are stopped when we've matched velocity with the local planetary surface. That works as a convention, but it is just a convention; it is not a truth. It is just as true to say that you are not stopped at all, but are "really" flinging around the sun.
In space, there is no such convention. Everything is stopped relative to itself. Everything is moving with respect to everything that doesn't share it's velocity. There is no referee who can blow a whistle and shout, "You, you're the one who's really stopped. Everyone else is moving."
No frame of reference is privileged over any other.
Still, objects are in motion, even if some objects are not in motion relative to other objects, and such motion would still seem to me to be independent of observers. Fascinating stuff though.
Independent of observers? I'm trying to think what you're imagining.
Imagine a two-body universe. Two asteroids tumbling. Is asteroid X moving and Y stopped? Or the other way around? Or both moving? There are no background stars to compare their motion to. There is no mark labeled "Center of the universe" that their motion can be compared to.
It is true that one or both is moving, because they aren't always the same distance apart. That fact is independent of any observers. But the notion that X is stopped and Y is moving is entirely dependent on whether you are X.