Think a bit more about a rigid body. Its atoms vibrate around the same fixed point. If they don't, you need to use the approximation of a fluid. If the fluid can be compressed, it is no longer a liquid but a gas.

It could be said, in truth and without scientific pontification, that a pencil is stationery even if it is moving. Hah, I couldn't resist.

That pun aside, yes I believe there is truth to your assessment that an item can be both stationary and non stationary at the same time. This would depend on the state of the item(s) to which you compare or measure it. Consider that Earth is in constant motion and therefore any item appearing to be stationary on it or non-stationary traveling through its environs could be said to be stationary in comparison to some other particles somewhere. Consider also that the atomic particles making up said object, stationary or not, are in constant motion (unless at absolute zero) making the item in question only apear stationary regardless of measurement or comparison to other objects or particles.