I think it depends on a person and his/her own vision of this issue. You cannot state, what an educated person means to everybody. For some people prefer to talk about general behavior and manners as of the education, some think of college and university attendance as a proof of being educated, some believe you have to gain knowledge on your own, no matter where you get it. There are also people, who might say that being educated means having enough experience to produce your own ideas.
So, I’d say you have to choose what does it mean to you. Like many people, as many opinions. I wouldn’t take somebody’s position as granted.
I won’t agree. To be an educated person means to continually develop yourself in each possible aspect, like mentally, morally, aesthetically. You have to look for new knowledge, gain it and use it as much as possible. For somebody to be educated, he or she doesn't really need to be really great in one specific field, but rather to have a decent amount of knowledge in a variety of areas. Such a person should be able to jump into practically any conversation and respond to almost every question, no matter whether it would be culture, modern tendencies or sports.
The word education, in essence, means to have the excellent schooling behind. So, you have to attend school and college to claim yourself educated. You, of course, can gain knowledge by yourself, skip education as a process performed in a corresponding institution, but that knowledge won’t be specific, and, most probably, it would be chaotic. How can you define which sources you may trust, where will look for good literature and examples of what you study? Yah, the Internet is full of materials, but they are not well-structured. And, the most important thing is, that you cannot learn from your teacher’s experience. Tutors know what they are about to bring and how to do it in the best way, for they have enough background to it. So, if you want to be educated, never skip the education itself.