Of course big brands have an advantage. That advantage starts with their financial ability to buy links, develop on-topic supporting websites for linking purposes and employing the staff to properly manage these sophisticated link building tasks. Because big brands have the financial capabilities to employ sophisticated link building schemes, they generally maintain control over the links that they create. Small businesses are more likely to participate in link building techniques that leave their links on websites that they do not have full control over. Once caught, the big brands can take down the links they created rather quickly.
Not only are big brands capable of removing their paid/built links quickly, once caught, but the reconsideration requests they send to Google are clearly reviewed much faster than small businesses. And the overall penalties these big brands receive for manipulating the SERPS with backlinks, in many cases, are not fitting for the level of sophistication used.
To say that big brands do not have the upper hand over small businesses is inaccurate. One need not look any further than how Google recently applied penalties, lifted penalties and responded to big brands in public to see this advantage.