If a btc exchange was richhhh..... couldn't it stabilize the price of bitcoins by buying some when there is a sudden excess of them on the market and releasing them slowly when there wasn't?
An exchange doesn't exist to speculate, it exists to make money off of those speculating. I don't want my exchange to be taking the other side of any trades. An exchange should not be exposed to exchange rate risk, for its customer's sake.
A party with a lot of money could leave funds at an exchange to try to stabilize the exchange rate. But that's capital intensive, and there are costs to carrying the capital. [Edit: And why would this "rich party" care to do this?]
The exchange rate had just more than doubled from a few months ago. This wasn't even a 20% pullback. Bitcoin used to see that level of volatility every other weekend, so it is just a matter of letting the market discover the price. Merchants who use a payment processor to convert to cash weren't affected by this. But obviously a volatile exchange rate isn't good.
When more methods for shorting bitcoins are made available then the exchange rate should level out a bit. There are a couple that I know of being built or are in limited (invite-only) trial currently.