Having a degree from Harvard or Yale would not make a non-native English speaker "equal to" a native English speaker. I don't see how you could imagine otherwise.
The non-NES would have to possess a great deal of their education in English, have practiced it extensively, and have lived in a NES country to learn a lot of the nuances/slang/idioms/etc., and even then, unless he has actually grown up there, he would not be "equal to" a NES. (In fact, to teach English in Japan, a non-NES must have 12-13 years of his education, all of his education, not just English classes, taught in English.)
Some non-NES's get a better English education than a lot of NES's, but that still doesn't mean they are "equal to" the NES.