Are lay articles good enough to be the main source of information for PhD research?
I find the entire premise of the question quite odd. First of all, to answer your question: I’d say that in most cases I’ve encountered the answer would be no, you can’t use popular science articles as a primary source. 

That said, I seriously doubt that they’re all that’s out there. Google works on this problem: they came up with it and no one else ever heard of it or studied it? How did the popular media hear about this amazing idea that has somehow eluded the entire AI research community except Google and your advisor? I feel like you’re either looking at the wrong sources, your advisor is not pointing you in the right direction, or something else is off.