GUIDING PRINCIPLE
The more supportive the environment, the more responsibility you can safely assume; the less supportive the environment, the less responsibility you should assume.
Regardless of the outcome, assuming responsibility means assuming risk and you need to be cautious, especially in a non-supportive environment.
Do you know when you are assuming reaponsibility for a particular outcome? It may be as uneventful as saying "OK" to a comment from your boss as you pass in the hallway. Most people are not even aware of what they have done or the potential implications!