Bitcoins, in private wallets, on the network, are increased through mining. Of course. But within an exchange, how many database representations of BTC is in that exchange may or may not have a corresponding reality with how many BTC the underlying exchange actually holds.

Since people aren’t holding their exchange balances in private wallets, it’s just a number in a centralized database of the exchange. Any exchange could trivially create more representations of bitcoins that they simply do not have and thus effectively create more bitcoins out of thin air, without mining. So long as the market participants don’t all want to move their BTC to their private wallet at once, this will work.

The exchange can also remove BTC from the market in the same way.

A plausible scam if you run an exchange would be to introduce new, effectively IOU imaginary bitcoins for sale when the price is high, and then buy these fictional ones back when the price is low, keeping the difference, and having equaled the books.

An opaque private exchange is just an asset IOU market — all the technological guarantees and safeguards concerning bitcoin and the monetary theory behind it go out the window, it’s just their property slips that are being swapped.