I found where I read that. Not exactly that Jeff Nelson started it but more or less coined the term within the band.
Quote:
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According to legend, the drummer for Minor Threat [Jeff Nelson], one of the first bands to preach the "stay punk, stay clean" ethos, ...was drawing a poster for a show using a wood ruler. He commented to his bandmates that the ruler's straight edge was a metaphor for their lifestyle.
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This is the URL not really a super reliable source but none the less where I heard it heh.
Straight Edge FAQ