I agree with you about connotations being relevant, but my sense is that the most important connotation here is "low status."

At least in the U.S., attributing 9/11 to Bin Laden/Al Qaeda is a relatively mainstream belief, as for a time was attributing it to Hussein/Iraq (although the two theories were not considered mutually exclusive among communities that embraced the latter); consequently we don't describe either as a "conspiracy theory" Attributing it to, say, Basque terrorists -- or even to the specific leader of an ETA cell, or whatever -- would be labelled a "conspiracy theory" if an otherwise unremarkable person did it, but not if the President did... or, more precisely, anyone who labelled it a "conspiracy theory" when the President did it would be attempting to lower the President's credibility/status by so doing.