A site I work for has tons of organic traffic coming from branded terms like BRAND, www.brand.com, BRAND + Product, BRAND + question, etc.
They also have a lot of non-branded terms, coming through. Overall a strong site.
I've also seen websites for lawyers on TV with plenty of spammy links, almost no good ones, but nonetheless they rank well for their terms.
My intuition says these are related, that the more people search for your brand, the more Google recognizes your authority relative to your keywords. Is this possible, or am I misguided?