I believe there must be lots of ways for institutions and companies to hide it: special purpose vehicles, subsidiaries, offshore accounts and companies, hiring agents, etc
I don't particularly disagree with this point
As it may or may not be true. If anything, let's assume for a moment that it is and institutions as well as companies hide their investments in cryptocurrencies. But then we won't know that, right? Therefore, their well-concealed investments don't mean a thing to us as we would still be dreaming of the times when institutional money would come to market, even though it has likely already been there for quite some time (as per our assumption)
For sure Institutions keep on holding the bitcoins and crypto at a cheap rate. They have the money to keep on accumulating bitcoin. When they have enough bitcoins, they spread positive news in the market and causes the bitcoin prices to rise. These are the Institutions who take most of the benefits when the price rises.