I guess it all boils down to:
Yes, anybody can get a Masters in design and probably get a job, but it is not the traditional way of doing it. And it seems it would be an uphill battle competing with the other designers that spend 2-4 years to get their BAs or BSs.
Yes, you can get an apprenticeship but I don’t know of anybody going that route.
Yes, you can learn on your own but you will be learning in a vacuum never knowing what you are doing right or wrong. Again, don’t know anybody that went that route.
I guess they see it as an MBA in a way. What they haven’t experienced or understand is the importance of your portfolio. What makes your portfolio is what you learn over the years and the thousands of ours spent doing different projects and learning from other people. Like everything it will depend on the individual his/her determination and the people around providing guidance.