except for the mild, easily predicted (and thus priced), and temporary decrease in supply following a difficulty retarget to a higher level, there isn't the slightest reason to think that rising difficulty should cause an increased price. there's no reason at all to think it should in the steady state.

as an analogy, if i'm pumping natural gas from an underground well, and someone else starts pumping gas from that same underground well in a way that doesn't change overall production but simply reallocates it, what effect do you think it would have on price?

any other effects people notice either confuse correlation for causation or posit some hard-to-measure empirical conjecture about the psychology of miners, none of which has proven to be true long-term, and none of which is grounded on anything but speculation.