No, not all experimental data require an "at rest" frame to be set with respect to Einstein's special relativity. The principles of special relativity apply to all inertial reference frames, regardless of their motion relative to each other. In special relativity, the laws of physics are the same in all inertial frames of reference.
Special relativity describes how physical phenomena and measurements change when objects are in relative motion. It introduces concepts such as time dilation, length contraction, and the relativity of simultaneity. These effects are observed from the perspective of an observer in one frame of reference, comparing measurements to an observer in another frame of reference.
Experimental data obtained in different inertial frames of reference will be consistent with the predictions of special relativity. The observations and measurements made by observers in those frames may differ due to effects like time dilation and length contraction, but the underlying physical laws and relationships will remain the same.
It's important to note that special relativity doesn't directly apply to non-inertial frames, which are frames experiencing acceleration or gravitational fields. In such cases, general relativity, Einstein's theory of gravity, is needed to accurately describe the behavior of objects and the passage of time.