Possibility one -- you have good data, but you're looking at post-tax income data, which would be skewed because of our flatter tax structure, fewer transfers, low long-term capital gains tax rate, and our relatively high income tax as percentage of total tax burden.
Possibility two -- the Gini coefficient you're looking at took national rates and then averaged them, rather than actually comparing incomes of specific people across the EU.
I believe that if you compared pre-tax data across the EU (rather than national data, averaged) you would see the EU having considerably more income inequality.
Just speaking from first hand experience, I've seen the difference between the lives of the wealthy and poor in the US (from Connecticut to Mississippi), and the wealthy and poor in the EU (from Bulgaria to Norway). The difference is much starker in the EU.
I'm sure it probably doesn't sound very scientific, but I'm inclined to trust my own eyes over statistics. If the data shows otherwise, I have to imagine the data is skewed in some way.