His groupings were based upon shared physical characteristics. Only his groupings for animals remain to this day, and the groupings themselves have been significantly changed since Linnaeus' conception, as have the principles behind them. Nevertheless, Linnaeus is credited with establishing the idea of a hierarchical structure of classification which is based upon observable characteristics.
I am aware of the history of classifcation. However, I was referring to modern taxonomy which as the passage you provided demonstrates is vastly different than that which was originally developed by Linnaeus. Mordern classification efforts are entirely based on the ToE, inevitably creating, as I was attempting to convey, a nested heirarchy. I guess the point I was trying to make was that the original posters arguement was moot because taxonomic classification as we known it today is premised upon ToE.
PS Thanks fro the warm welcome.