The demagnetized skin depth width electron diffusion region (EDR) distinguishes the innermost current layers of collisionless magnetic reconnection (CMR) from other current layers. Such narrow layers with virtually unknown properties are hard to identify in space observations. Soon, diagnosing it will be the central focus of NASA's Magnetospheric Multiscale Mission. Initial attempts have been made to frame necessary tests to ensure that the observer is in the EDR. Since none of the tests are sufficient to identify the EDR, it is important to vet as many necessary conditions as possible. In this way a winnowing process can lessen the likelihood of false positive detections of the EDR. Since the “necessary” criteria of the EDR are usually not amenable to direct experimental tests, a vetting process is desirable before accepting “necessary” proxy tests for the criteria of CMR. This paper proposes a further necessary test of an essential property of the EDR: the necessity that the thermal electrons be demagnetized in these regions. Without this attribute, the magnetic flux is essentially frozen to the electron fluid velocity and the topology breaking of CMR is thwarted. We have framed this test from kinetic theory, gathered the relevant observables, and used it with a published set of over 100 previously identified EDRs. Surprisingly, 99% of them are ≃100 times more magnetized than expected for the EDR of CMR theory. The outcome of this falsifiable test demonstrates the scientific dialogue is incomplete for framing adequate pragmatic tests for identifying EDRs.