Shows that there must be a Preferred Frame (PF) or set of PFs where clock rate (i.e., proper time accumulation) is the fastest.
Step 1: Note that the data shows that all clocks at rest in the same frame, other things being equal (e.g., same gravitational potential), have the same clock rate (i.e., accumulate proper time at the same rate). [This is the basis for having the standard second, etc.]
Step 2: Next consider two cases:
1) All frames have the same clock rate. Data showing net proper time differences argues against that assertion.
2) All frames do not have the same clock rate. If that's true, then the frames can be ordered by clock rate yielding a hierarchy where a frame or set of frames will have the fastest rate and where another frame or set of frames will have the slowest rate. One can label the former as the Preferred Frame (PF) or set of PFs.
Note 1: From the limited logic presented above, one could contend that the hierarchy of frames consists of randomly ordered frames. However, if when we changed our state of motion slightly, a large shift in clock rate occurred, we'd have likely noticed that. Hence, there is informal empirical evidence that the hierarchy of frames is ordered by velocity (e.g., with respect to the PF) such that a small change in velocity produces a small change in clock rate, etc...
Note 2: Some who do not like the conclusion want to add complexity to the above, however, those complexities turn out to be completely irrelevant to the basic point. One can choose to understand the point or to ignore it. If one does not like frames because one does not like Special Relativity's treatment of frames, then, for example, one can substitute "state of motion with respect to a specific object or field" for "frame" and the basic point remains valid.