System Information
Windows 7 Pro 64bit
Blender Version
Broken: 2.75a c27589e
Worked: 2.74 000dfc0
Unable to remove Action neither by Shift + [x] button as in 2.74, nor by removing users, nor by deleting from NLA, nor with combination of the all methods.
Video explains it all:
https://www.youtube.com/watch?v=-txwhEpx7DQ
Blend file:
Potential solution: Please bring back Shift +[x] from 2.74. It's hard to accidentally delete Actions, and it's easy to remove them when needed.