Just my two cents on what makes a degree like a PhD significant over "at home" independent research via the internet:
Since most grad programs require you to do some teaching, that absolutely forces you to know your shit really well. Now, even though the material you'd be teaching is only undergrad level, the experience teaches you the value of more thoroughly knowing and understanding the material, which will surely carry over into whatever you're actually working on for your degree.
There is also something to be said for having to meet deadlines. Most people don't already have the kind of discipline to be able to go through what you have to go through when doing an advanced degree. Having to meet deadlines forces you to learn discipline in your work.
But I don't just mean discipline with respect to getting it done within a time frame. Since you do have a limited time frame, you are forced to learn how to do disciplined research, in the sense that, you have to be more rigorous, more focused; you have to be able to have a sense of the quality of the work of others, to decide whether you can rely on it as a source.
Perhaps most importantly, you get grilled. You have to work with a mentor or advisor or whatever you want to call them, and you have to, on several occasions, present your work to him or her, and they will regularly critique your work, both positively and negatively. (In fact, it's never just one person; usually a few.) And especially with a PhD, that doesn't just happen regularly while you're working on your dissertation: when you're finally done with the thing that has dominated your life for 2 or 3 years, you have to then go through the finale: your defense! It is pretty much the job of your advisors and other professors and colleagues to grill you in your defense.
One of the things I am most grateful for from grad school is that I learned how to research, learned how to learn about things that I was not previously familiar with. Grad school taught me the skills I need to be able to research on the internet and try to learn "on my own". I mean, there is definitely a world of difference between how I did research in undergrad - and the internet was much, much smaller then! - and how I was doing research in my last couple of years of grad school.
But, even though I say I know how to do research and learn "on my own", I would never claim or even think that I could have nearly the same amount and depth of knowledge and understanding that someone with an advanced degree has.