Khan Academy is obviously a useful tool for learning, and of course it's part of a child's education, not all of it. The point I think Dan is making is that if you 1. say you're aligned to the common core, and 2. provide mastery statistics to suggest a level of comprehension or depth of knowledge tied to those standards then that should predict well a child's performance answering questions aligned to the standards but outside the KA system (e.g. a Smarter Balanced Assessment)
That means until that ideal is reached KA could say "Mastery at X depth of knowledge but note, for this standard Y is required" or allow teachers to write free response questions and have them tag the questions by standard, type, depth of knowledge etc. and grade them by hand in the KA system. Including hand graded questions (by a student's teacher)with an adequate tagging system KA mastery statistics might be significantly more accurate.