No, it doesn't. That info from the website is a gross mischaracterization and seemingly an attempt at self-promotion. It's like saying that your building has walls and a ceiling and is therefore in the same league as Notre Dame de Paris and the Taj Mahal.
As an example, some of Corinthian's colleges (Heald College) were accredited by WASC. . . until they declared bankruptcy in the face of multiple fraud investigations and a $30 million fine.
The accreditation is an extremely low bar. In my view it is so low it is harmful because it totally fails to distinguish legitimate schools from shady ones. Accredited colleges run the gamut from the sublime to the ridiculous.
That's not to say the school that this article is from is bad. I don't really know anything about this school. But the fact that they tout mere accreditation as putting them on par with Stanford and that they can't correctly name the University of California, Berkeley does not inspire confidence. The fact that it is nonprofit is a plus, though, as the worst of the crap-but-accredited schools are for-profit ones.
That tells me something