I believe that if you truly understood how exchanges work, you wouldn't hold this belief. I guess I should elaborate. You may know some of this but you likely don't know all of it.
There are two types of orders: LIMIT and MARKET. Limit orders get added to a list. There is a list of standing BUY orders and a list of standing SELL orders. They are standing/LIMIT because no one has taken them up on their offer. For example, I can enter a limit order now: "I offer to buy BTC for $500."
You can only enter a LIMIT SELL order at 1 penny above the highest BUY offer or higher. Conversely, you can only enter a LIMIT BUY order at 1 penny below the lowest SELL offer or lower. This is because when you TAKE an order that already exists on the book (the lists), you execute a MARKET order, not a LIMIT order.
Executing a MARKET order means that you "eat up" the book/list until you have reached your order size. So if I place a market order to buy 3 BTC I will progressively buy BTC at higher and higher rates from the standing limit sell offers until my order is fully filled.
That is how an order book/market actually works. Now enter your claim:"Market manipulation. The prices are really set by the coin exchanges"
What exactly would this entail?
I guess you suppose that Coinbase simply increases the price of Bitcoin on their website, and pockets the difference between what people pay and what they acquire them for. Clever!
But wait a minute, in order to increase the price, they have to eat all of the orders between the starting price and the finish price. Otherwise people would notice that the price moved over their order without filling it, which should never happen, and which would thus prove fraud, which would probably completely destroy the company.
So Coinbase, knowing this, decides to eat up all of the orders from the original price (let's say $15,000) to the new price they want BTC to cost: $20,000.
In order to do this, Coinbase has to OVERPAY for every single coin they buy on the way up. There is a fair market price, which is what you can expect to get when selling a coin, and you would have to agree to pay above this price for every single coin in order to manipulate the market. As a result, your attempt to manipulate the market would almost certainly lose you a massive amount of money. The order book has a lot of orders in it. This appears to me to be one of the stupidest things anyone could ever try to do. It would move the market, but it's not clear that there's any reason to believe that it would be anything but massively unprofitable.
Imagine walking into a gold market and offering to buy all the gold that's for sale at higher than the current fair price. Wow, what a clever strategy! Surely you'll make a killing!
It doesn't really make any sense.