Huh?
Forgive me, but what exactly is the original question? Is it..."Do Americans who self-identify themselves as 'white' actually have upwards of 30% saharan DNA"? Being a member of 23andme and deCODEme, and frequent forum contributor to both sites, I would say absolutely not.
I think that African Americans often have 30% (or more) of European DNA, but your average WASP (euphamism for White Anglo Saxon Protestant, but I'm using it in the place of average white person from the USA) has little, or most often no Saharan or Asian DNA. deCODEme is more generous w/Asian and African DNA and most self-identified Europeans have a small percentage of each. Me: 100% Euro 23andme; deCODEme 97% Euro, 3% African and Asian. I have recent immigrants as ancestors (post 1850), and folks from the colonial period seem to have a higher chance of both African and Asian (native American) DNA, but nowhere near 30% based on the many posts on the subject.
So the obvious question is if blacks have a substantial amount of Euro DNA, then surely whites must mirror this, right? No...at least not yet. You have to realize that segregation was common, and mandatory in some states and marrying between races was very uncommon, and illegal in some states. This only started to change significantly in the 50's and 60's. If a mulatto child was born, that child was considered black, most likely segregated in black communities and had children within that community. There were exceptions of course, but for the most part, DNA flowed one way between white and blacks in the US, and stayed that way for a long time. I suspect with changes in society, and some time, you'll find that will change.
So, in conclusion, I think that 30% is not for "white" people, but actually "black" people from the USA.