Obviously this is just one more anecdote, but this exact same thing happened to me on the Iberia website about two years ago, while looking for flights from Europe to South America.
I kept track of my searches in a spreadsheet, so I know for a fact that the price went up slightly (I think it was by 20€), and went back down immediately when I switched to a different browser.
Again, this was unfortunately too long ago for me to have reasonable proof, and it hasn't happened since (perhaps because I now tend to avoid Iberia anyway; they're pretty crappy in other ways as well).
I kept track of my searches in a spreadsheet, so I know for a fact that the price went up slightly (I think it was by 20€), and went back down immediately when I switched to a different browser.
Again, this was unfortunately too long ago for me to have reasonable proof, and it hasn't happened since (perhaps because I now tend to avoid Iberia anyway; they're pretty crappy in other ways as well).