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?
There is already a lot of evidence that leads there, starting from the purchase of very large bitcoin, which is enough to move the market price, as said by gabmen. Not a few of them who are involved as disseminators of FUD whose purpose is solely only to cause panic both through Infotainment media and the internet. Exchange, I'm very sure they have great potential as one of the popes for example tether.
It isn't that hard to figure that out even if you don't have actual evidence. Logically, if you have enough coins to manipulate the market to your advatage, why won't you? And i think there have been several instances where a single transaction from the same wallet address bought or sold enough coins to move the market.