I have not thought this through fully, but could not the sentence be read in either of two ways:
- He is one (of the men) who do/does the work.
- He is one of (the men who do/does the work).
The verb form would be singular in the former reading, and plural in the latter.

And it would seem to me that there's a subtle difference in meaning between the two sentences, though I cannot put my finger on it. Comments?