Jack, I had the same error without placing files in the wrong location that you did. I have Moodle 1.9.2 (Build: 20080716)
This is the first time in a long time I have viewed the certificate function (have been recording the class that the Moodle site supports) so I can't tell when it went wacky.
Your solution resolved the problem though - and for that I thank you!
Custom certificate (plugin)
FPDF error: Some data has already been output, can't send PDF file
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