The authority page on William B Bradbury lists "He leadeth me" among the "texts by Bradbury"; Bradbury composed the tune, but he did not author the text. I haven't checked to see how many of the other listed "texts" ascribed in that list to Bradbury are actually texts for which he composed tunes. But I'm guessing it may be quite a few. Not to say that he couldn't write...
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Bradbury and He Leadeth Me
One DNAH hymnal that we haven't looked at yet lists Bradbury as an author. That is the reason "He Leadeth Me" shows up under Bradbury. The text authority has Gilmore as the author. We will need to look at the hymnal before making any corrections. I'm sure there are many other similar misattributions in Hymnary