Unfortunately this is plausible: The only reliable way to trigger a run-up in a commodity is to expend a lot of capital to acquire that asset at inflated prices- You'd have to "burn through" a lot of money to get this to happen.
...so, then where was this cache of money that was destroyed to inflate the price? It would have to be a pretty large quantity to have such a drastic impact.
Occam's Razor to me suggests the answer is obvious: The vaporized deposits of MtGox users are the most obvious large cache of money, large enough to cause such a run up.
The next question is, who would do this, and why? The answer suggested by Occam's razor would be "Someone who could modify the MtGox database to create nonexistent fiat currency, but could not (or did not want to) create fake MtGox bitcoin holdings." This is because a person with this power would have reason to trade the "fake fiat" with legitimate bitcoin holders to generate bitcoins that can be leeched out of the site, and this would certainly cause the price to rise.
This doesn't answer however whether it was an inside or external party, I could imagine scenarios both with or without inside actors that would lead to this kind of activity. (Though I'd put my bet on internal fraud, based on the fact that so much effort was put into hiding the fraud and extending it over a long period, as opposed to going for quick profit.)
Doesn't seem obvious to me at all. As a result of bankruptcy proceedings we know that Mtgox has lost primarily BTC deposits, not fiat (on mobile now, but IIRC only $27 million USD was lost which is peanuts compared to the value of lost BTC)
In other words, the situation at Mtgox was the opposite of what you describe: it had a lot of FakeBTC, bit its USD reserves were mostly real.
Whether or not the run-up was "legitimate" in your eyes is inconsequential - the exchange rate ran up to the point that the market could no longer bear, then crashed back to reality. Does the run-up's legitimacy somehow make the current exchange rate illegitimate? I think not.
Actually, the rate ran up to the point that Mt. Gox could no longer bear. Unfortunately, it's rather easy to start an exchange and get people using it (or at least, it's no more difficult than any other startup) so there will probably always be companies willing to manipulate the market for personal gain. And since every popular exchange's price affects every other, manipulation from one will manipulate the price at all the rest.
The modern day bitcoin trader should carefully consider whether they want to be a part of a market where the largest actors aren't bound by the rules they set for everyone else.
Though I agree somewhat with your argument, a true "legitimate market" requires full transparency by all parties without people trading on insider info.
In this case, however, only some parties knew that MtGox's internal accounting was broken. Therefore, the price run up may have been "illegitimate" for a limited time period based on this asymmetry of information.
You are right though that over the long term a market price is always "legitimate" by definition, because of the maxim "something is worth whatever someone is willing to pay for it."
like all ponzi schemes, it relied on new users getting sucked in. As other exchanges grew and Mt Gox doubts spread, I imagine their growth rate dropped.
...so, then where was this cache of money that was destroyed to inflate the price? It would have to be a pretty large quantity to have such a drastic impact.
Occam's Razor to me suggests the answer is obvious: The vaporized deposits of MtGox users are the most obvious large cache of money, large enough to cause such a run up.
The next question is, who would do this, and why? The answer suggested by Occam's razor would be "Someone who could modify the MtGox database to create nonexistent fiat currency, but could not (or did not want to) create fake MtGox bitcoin holdings." This is because a person with this power would have reason to trade the "fake fiat" with legitimate bitcoin holders to generate bitcoins that can be leeched out of the site, and this would certainly cause the price to rise.
This doesn't answer however whether it was an inside or external party, I could imagine scenarios both with or without inside actors that would lead to this kind of activity. (Though I'd put my bet on internal fraud, based on the fact that so much effort was put into hiding the fraud and extending it over a long period, as opposed to going for quick profit.)