The ambipolar-diffusion theory of star formation predicts the formation of fragments in molecular clouds with mass-to-flux ratios greater than that of the parent-cloud envelope. By contrast, scenarios of turbulence-induced fragmentation do not yield such a robust prediction. Based on this property, Crutcher et al. recently proposed an observational test that could potentially discriminate between fragmentation theories. However, the analysis applied to the data severely restricts the discriminative power of the test: the authors conclude that they can only constrain what they refer to as the ‘idealized’ ambipolar-diffusion theory that assumes initially straight–parallel magnetic field lines in the parent cloud. We present an original, self-consistent analysis of the same data taking into account the non-uniformity of the magnetic field in the cloud envelopes, which is suggested by the data themselves, and we discuss important geometrical effects that must be accounted for in using this test. We show quantitatively that the quality of current data does not allow for a strong conclusion about any fragmentation theory. Given the discriminative potential of the test, we urge for more and better-quality data.