I've seen that stated before, and Wikipedia seems to agree, but relatives of mine used to live there and I've always heard it as 'Mill-guy' rather than 'Mull-guy'. Is this perhaps another Shrewsbury-type situation? Or maybe it depends on one's accent, or I (or closer relatives who never lived there), have been led astray by the spelling (the unstressed syllable is probably more prone to drifting).
On the subject of Shrewsbury, other relatives of mine lived in southern Shropshire for many years (although not originally natives of the area) and for what it's worth 'Shrowsbury' is what I've always heard.