I don't think the openness of a country has much to do with the number of conspiracy theories that form about it.
Conspiracy theories find patterns in incomplete data. There is always incomplete data, and there are always patterns to find. IF you get deep enough into them, then you can even turn around and point at evidence that disproves your theory, with the claim that actually, it proves it!
Just the other day, I responded to a post on HN that claimed that there's a vast conspiracy by the Labour Bureau to hide unemployment numbers, by reporting only the U3 numbers, when the U6 numbers are more relevant.
When it was pointed out that the bureau reports the U6 numbers, as well as the U3, the claim turned into 'Well, its obviously a conspiracy - what better way to hide the truth than to conceal it in irrelevant gibberish!'
No amount of openness is ever going to dissuade that kind of intellectual dishonesty.