You don't have to buy BCO, but you do need to have a small amount of BTS (Bitshares) to pay for transaction fees, since every action you perform on the exchange happens on the BTS blockchain. I believe you receive some from a faucet when you create a new account and they can be purchased for very cheap on the exchange ($1 worth of BTS can last for months).
Excellent.
So Bitshares to trade, BCO to get a stake in their company.
It's great how far decentralized exchanges have come.
I made a few trades there and used up the free BTS I had in my account but still had a few trades I wanted to make. It just took the fee out of the coin I was using to trade. So you don't really need BTS, apparently.