Is there any evidence that these mysterious 'whales' really control the bitcoin market, or is this a myth generated as people try to understand why bitcoin prices go up and down?
Not a myth or a figment. Given that bitcoin which is not authorized by government legal entities, has made it vulnerable to manipulation by a group of big whales. Large whales are more camouflage they can be behind anyone, for example CBOE, exchange sites or companies, etc.