Ferromagnetic sheath around a superconducting wire results in an unusual transport Jc(H). For the field perpendicular to the current, there is a plateau in Jc(H) at high temperatures and intermediate fields. This plateau develops into a peak at lower temperatures, resembling a “peak effect”. A model based on cancellation of the self-field of the current and external field within the iron sheath was proposed for the explanation of the plateau in Jc(H). We test this model in three key experiments. Firstly, we show that the form of Jc(H) for round MgB2/Fe wires is strongly temperature dependent. This is in contradiction with the model, because the properties of the iron sheath do not change in the measured temperature range. However, the temperature dependence of Jc might still account for the change of Jc(H). Secondly, the model requires a substantial component of the self-field to be parallel to the external field. Our measurements of Jc(H) for field parallel to the current show a peak in Jc(H) at high temperatures and a pronounced plateau at low temperatures. The model cannot explain this because the self-field and external field are perpendicular in this experiment. Thirdly, the iron sheath was made thinner on one side of the wire, which should produce an asymmetry in Jc(H) in the model for two different orientations of external field. Such asymmetry was not observed. These experiments show that the effect of the self-field is of much lower importance than a yet unknown effect that results in the observed plateau and peak in Jc(H). Such effect is likely to be based on a specific interaction between the superconductor and ferromagnet, perhaps similar to the overcritical state effect.