In the beginning of Bitcoin, did difficulty come first or did price? The answer is difficulty started going up before Bitcoin was even worth anything, therefore price follows difficulty.
That's not even an argument. You could ask yourself if you think early miners mined for profit. Obviously there was no economic incentives involved until bitcoin had a price.
Anyways, no need to disprove anything, some guy already did it:
http://divananalit.org/Data is clearly showing the opposite of what you claim.
