Why should Europe NOT be independent and America still be granted to intervene when they see fit without NATO on their side? If they were really the great heroes they dissimulate to be, why not lift their invulnerability against war crimes? Anyway, America is not the issue here. So I won't address that anymore(you can still reply of course

).
Back to the point:
'there will be no duplication of NATO's role and that NATO will remain as Europe's primary defence organization.'
'European Union countries have pledged the troops and equipment required to launch a new Rapid Reaction Force which will take on conflict resolution, peacekeeping and humanitarian duties where Nato chooses not to get involved.'
In other words, it's supplementary. It does
not undermine any healthy position the NATO may or may not have. It adds to the solution of a problem.
'The Americans, the dominating contributors to NATO, have long called for that organization to shoulder a bigger proportion of the defence burden in Europe.'
Source:
http://www.cnn.com/2000/WORLD/europe/11/20/europe.defence/index.html