Well, since I have a Masters in Financian Engineering (well, technically, a Masters in Computational Finance -- but same difference), I feel like I at least have to comment on a few things.
1. Just because the material is freely available on the internet does not mean you will have the ability to learn from that material. However, an inability to learn the material does not necessarily indicate a disinterest or an ineptitude. Quite frankly, it took the threat of a grade and the commitment of paying tuition for me to sit down and read through Shreve's Stochastic Calculus books, despite the fact I had picked them up almost a year before attending CMU.
2. Reading a bunch of books doesn't make you knowledgable on a subject. Deep interaction with the material does. You don't go to school just for a piece of paper -- you go for a structured learning environment. I went because I believed, and still do, that the teachers who understand this material will know the best way to organize and present it to me. Furthermore, most MFE programs stress the importance of an internship, giving students pragmatic experience. Finally, most MFE programs also offer speaker series to provide interaction with industry practitioners.
3. Whoever is saying 'Girsanov's Theorem' doesn't understand the connection. Girsanov is only relevant from the Fundamental Theorems of Asset Pricing, which is only relevant in that it translates the question of arbitrage into a question of existence of a risk neutral measure. Ultimately, pricing is merely replication.
4. "So you’re trying to get a job where you face the market everyday and disagree with it." This quote tells me you fundamentally are misunderstanding what occurs on most Sales & Trading desks, which is where most people from MFE programs try to place. Don't worry -- most people don't understand what they do. Quite simply, most Wall Street traders do nothing other than execute trades for clients and try to match and offset the risk of the trade with other clients. Sometimes traders will carry some risk in their book (most of the time, it is second-order risk) -- but for the most part, they aren't actively taking bets on market direction (though, rumor has it Goldman is notorious for this…) -- they leave that up to the hedge funds.
5. This whole notion of independent thought versus 'indoctrination' is ridiculous. I'm sorry, but math is math, whether you read it on your own or are taught by a professor. Independent thought is a characteristic of the student, and they either have it or they don't.
6. Is the degree expensive? Heck yes. Is it worth it? Only you can answer that. For me, having the degree is priceless because I own my business, and it acts as a certification of qualification when I meet with clients. It serves as one more point for them to check off in their due diligence on me.
7. You will completely miss out on the opportunity to network with peers. I now know people who I worked with on a daily basis at almost every major Wall Street firm, from investment banks to hedge funds to consultancy firms. That is a priceless network.
So can you learn the material all on your own? Sure -- but I bet it takes you a lot longer than the year and a half it took me. By going to school, I was able to dedicate myself full time (homework and classes well exceeded 40+ hours a week), to learning the material. In my opinion, this isn't really material you can learn 'part time,' and if you try, you certainly won't have the opportunity to develop any practical understanding of it.