He can only "own" the market of his own block. There are a variety of filters that could be used to remove the "noise" of an attacker - signal analysis is a field in itself. For the purpose of explanation, I will give a simple unsophisticated filter: take the median of the last N blocks. That is to say, for each block determine what the average price is of the market you are interested in, and then take the median of those values over the last N blocks. The attacker or cartel of attackers needs >50% of the hashrate in order to reliably affect the median value. Observe that an "attacking" block is one whose inferred pricing deviates substantially from the actual order book known by other miners due to wash trades, and that difference would be observable.
We're talking about network-level sybil attackers; this isn't about hashing power.
You can also think of this as a machine learning problem: you use unsupervised learning to group blocks into labeled buckets representing the underlying order book, and then choose the bucket which represents the most work over the last N blocks. You then compare that price structure with the orders you are seeing in the order-publication medium (p2p network, bitmessage, whatever) and decide whether you are being cheated or not.
That's vastly more complex and unreliable than having proof-of-publication available. After all you don't have to use it exclusively, just enough to detect and discourage attackers. Note how if we create a H(prevout) based CHECKSIG mode where the txid is not hashed you can arrange for a completed trade to prevent publishing of the trade itself separately.