This is very annoying. I need to delete an action I keep hitting x and clear animation data and all that, won't leave! I have quit and reopened, there is no 0 next to the name.
To unlink datablocks from the blend file hold Shift button and click on the X icon of the datablock. That will set the number of users to zero and it will not be saved in the blend file.
Remember to reload file after saving it.
here you can use this version of blender and holding shift while pressing the x (next to the animation in the action editor) will remove the fake user not sure what changed between the updates but i know this one works
blender version 2.69 http://download.blender.org/release/Blender2.69/