> The people who would receive the BI are the in the lowest income brackets.
As I understand BI, this is not true. BI is a payment made to every citizen and/or resident of a country, irrespective of any other consideration (including income, wealth, etc). What you seem to be describing is Guaranteed Minimum Income, which is an entirely different ball of wax. I'm now wondering how much of the discussion is people talking past each other because of conflation of these two terms.
See http://en.wikipedia.org/wiki/Basic_income and http://en.wikipedia.org/wiki/Minimum_income