Source: p x, How Can You Represent Those People? (2013) by Abbe Smith, Monroe Freedman (Editors)
Prominent criminal lawyer Edward Bennett Williams [ (1920-1988) ] once noted that, like other criminal lawyers, he took on difficult cases for unpopular clients, “not because of my own wishes, but because of the unwritten law that I might not refuse.” The lawyers in this collection could not refuse either. Moreover, they could not be prouder to champion the very worst of “those people.”
The 20th-century (20c.) meanings of (the past-tense Modal Auxiliary) might appear to contradict Williams's meaning above (the unwritten custom or maxim prohibits refusals to be based on unpopularity of the defendant), because they express possibility or suggestion, contrary to the decisive, dominating, and officious connotation that Williams needs (to emphasise the disapproval against refusal).
So did Williams use the incorrect Modal Auxiliary? I would have used (the Present Tense Modal Auxiliary) 'must'
Or I thought of this more charitable, forgiving but improbable possibility: Maybe Williams intended meaning of (the etymon of 'may') the Old English magen "to be able"? Then the bolded might would mean 'was not able to' which would accord with the context.