The logic there being that you want to test (to stretch to failure) the threaded rod, not the test fixture itself nor the test clamp for the rod.
So, to exaggerate slightly, if your test clamps were threaded, and were made out of some material less rigid, and overall less strong than the threaded rod, the test fixtures would bend and distort before the rod would.
Now, what are you trying to test for actually?
The threads themselves as a stand-alone failure point? If so, then your assembly needs to remove as a failure point everything except the tips and roots of the threads of the "average" rod.
The final tensile strength at failure of the (average ? minimum? Maximum? Nominal? 5 sigma deviation weakest?) rod? How will you define average rod material strength and average thread and rod dimensions? How many rods will you use to develope your std deviations and statistics? How will your tests vary based on changes in rod threads and rod dimensions, compared to rod material deviations? And, how will you tell the difference when each rod has failed?
The tensile strength of an (average) threaded rod held in place by an (average) nut tightened to an (average) torque value? After all, if a nut is held in place by tension, doesn't that tension increase the local stress in the rod-and-threads that can induce failure of the assembly? So, shouldn't you be worried about how much the assembly can hold, not how much a rod itself will fail at?