I agree with the point that a small or medium-sized business will have limits for budget and resources in generating brand search, but I wouldn't say that stops them from potentially producing huge growth there if they do something interesting/innovative etc. I can think of quite a few small to medium sized brands that have more name recognition than larger companies in their space. The challenge is that many of those brands are led by people who are very good at generating marketing and publicity - it's harder for small brands to be able to afford to pay for a top level consultant or agency.
At our agency, we work with sites of varying sizes, from very large to quite small, and recently, we have noticed a trend at the enterprise level. These sites aren’t relying as much on Google for traffic any more. Not only are they not relying on Google traffic, but also, the sites are getting less than 10 percent (or slightly more) of their organic traffic from the search giant.