What prevents a witness from publishing an extremely exaggerated price feed?
nothing, other than potentially losing the support of those who delegated him (it's DPoS, not PoS)
What is the final median value used for?
For setting up the internal price of STEEM
What do you mean in your last sentence?
From your question I understand that you think witnesses are publishing price feeds for the STEEM they own, like an offer for selling their stake, and that is not true. Also, there is no price difference in buying from a witness or buying from a normal persons. Price feeds are like oracles.
Much of this information is in the white paper. I highly recommend to read that a few times to familiarize yourself with the ecosystem.
So the internal price of Steem is not determined by buyers and sellers like in Exchanges where a buy order price limit has to meet a sell order price limit?
Internally, price is set up by witnesses. Of course, witnesses are weighing in what happens in external exchanges when they publish their price feeds. But there will always be an arbitrage opportunity if you follow the internal market closely. I saw gaps up to 30% between SBD/STEEM internal vs external, in both directions.