I would agree with you on all of that. You said it just like it is.

It can be anything from designing buttons for your web page to designing banners, pictures, print, and graphics for things like video games and alot more. Graphic Design can cover quite a broad area just like Web Design can.
As for the qualifactions, I really think all that matters is the skill, talent, and like with all other things the ability to perform.

Education and training can definitely help and will most likely make you more qualified, but there are many that are excellent at graphic design that have never had any certification, training etc. In the design community people will pay for graphic design based on previous work and recommendations, all that matters is that they can do what you want with the graphics and do it good, most wont question qualifications, but would rather just see example work and proof that they can do what they say they can.

But for graphic designer wanting to get a job with alot of companies they'll usually be required to have the training certification experience etc....
