"You've always gotta do things your way, don't you. No wonder Briggs stays on your tail."
"Do things someone else's way and you take your life into your own hands."
~Harry responding to his partner in Magnum Force
Harry seems to be making a counterintuitive remark here. To take one's life into one's own hands is to take responsibility for one's actions in the most extreme way. Yet Harry here implies that it is precisely when you are following the suggestions (in this case explicit orders) of another that you are most responsible for your actions.
Conversely, the claim seems to be that responsibility of the take your life into your own hands sort is avoided precisely by doing things one's own way.
Of course, this goes against common sense attributions of blame and agency, and is a direct converse of the "deep self concordance" model of blame attribution. That model claims that attributions of agency and blame occur when there is an agreement (concordance) between the agent's actions and his deeper commitments and value judgments (i.e. his "deep self").
Here, Harry expounds the opposite - when you act in a way that disagrees with your deeper ideological commitments, then you are the one to blame for the consequences of those actions.
I think the positive suggestion behind Harry's claim is that there is something blameless about acting in accordance with one's deep seated beliefs. If we act against our instincts / values / ideology, then we are violating a fundamental principle of authenticity - we have voluntarily given over control of our actions to another source, one which we, at a deep level, disagree with. This knowing abandonment of authenticity does not free one from blame, but rather that act itself places the weight of responsibility more heavily upon one.
As a corollary, acting authentically, i.e. in accordance with one's deep seated beliefs, frees one from blame—or, at the very least, constitutes itself an explanation and justification for one's actions: "I did it because I thought it was the right thing to do."