Just that coders who get shit done are often not the A-people. We had a few people that get shit done, and their code was shit. So in the end they cost us more time and money since we had to refactor large parts of their code.
Absolutely! At Qype we have a few very good Ruby on Rails freelancers who did not study CS (one studied design) or didn't even study at all i.e. are self-taught.
You should definitely also consider doing freelance work, because no-one would ask for your degree anyway, all that matters is your skill. From my personal experience, however, it's unusual to find A-people in software who do not have a CS degree. They exist, but I think they're the exception rather than the rule. Often people without an academic background in CS lack the understanding of some fundamental concepts that underly almost everything in computing. They know how to write code and perhaps even what code and architectural patterns are, but they apply them without understanding the inherent principles that underpin them (there's only a handful of rules for instance to which all object oriented design patterns can be reduced to, such as abstraction of change.) On the other hand, I interviewed many people with university level degrees in CS who were not good at all. So a fancy degree is definitely no guarantee for skill.
If you apply, as you already mentioned, show proof of skill e.g. by linking your GitHub account. Good companies will make you do some sort of code or technical challenge anyway, so degree or not, all that matters is that you're good at what you're doing. I would also strongly encourage you to not only read books on programming language or frameworks. Bad developers focus too much on implementations rather than concepts. Technology will be replaced after a few years anyway, but if you have a good grasp on a few fundamentals of software engineering and software architecture, you will soon realize that every new technology introduced is usually just building on insights that have been around for decades (MVC frameworks for instance) and just take a slightly different angle at things.