It is not NATO that hinders the ability of Europeans to act indepedently, but the political determination of Europeans not to act independently.

Specifically:

• national governments have denied knowing anything about the CIA flights and prisons, and have not complained to the US for violating their laws or international treaties such as the Chicago Convention on Civil Aviation. National parliaments have not carried out investigations. The European Parliament doesn't have subpoena powers, while national parliaments do. However, in parliamentary systems the government generally controls the majority faction in the parliament.
  
• The EU battlegroups require NATO resources to be deployed because they have been designed not to duplicate existing NATO structures, again by political determination of EU member states involved in the CFSP.
  
• The EU can build its missile defence system without consulting NATO because it can do it through bilateral agreements. NATO member states have made a political decision not to complain too loudly. In addition, Jan de Joop Scheffer doesn't oppose the missile shield. When Merkel started making noises against it last year, he came out defending the need for it to deal with threats from rogue states, and after a NATO meeting at which no member state voiced any objections, Germany fell into line.
  
• Galileo: the European Council was more than willing to kill Galileo and satisfied with depending for civilian navigation on the US' GPS which is under military control. This is again a political decision at the level of national governments.

See my signature.

We have met the enemy, and he is us — Pogo