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?
Market manipulation has existed for years. It was not invented by the media or something. Every market has significant players who can influence the market due to the amounts they have. So the phenomenon is quite old and well-known, but they do not call themselves 'whales,' of course. The name was coined by the media, I believe, but that does not mean the media have invented them. The media might have invented their name, i.e. 'whales,' but that's it.
This is my understanding of it as well. Basically once an entity has a large amount of money they can now be an "influencer".
From there it is all strategy.