Here is my view on the matter:
I've heard people say, when Muslim X does bad action Y, that Islam isn't to blame for Y.
The reality is Islam is not to blame for the action of that said person. Let me explain, for instance one can call themselves a Muslim, and not hold to the faith strictly.
Example: A Muslim drinks alcohol, and becomes intoxicated, then proceeds to get into a car crash.
The Muslim did commit a bad action, and Islam is not to blame. This is because Islam strictly motions that alcohol is prohibited for a Muslim, the blame lays only upon him, not his religion as his religion clearly is not tied to the bad action.
From the perspective of Muslims, does a person's religion influence their behaviour?
For me my religion does shape who I am, it limits me from my primal urges, without limitation I would assume that my behaviour would be radically different without my religion, as there would be no reason to limit my urge so that certain thing. Islam is also a constant reminder to me that enforces certain behaviours as well, such as that I have patience with others; do good, pray five times a day, and many other things.
On other things:
I've heard people say, when Muslim X does bad action Y, that Islam isn't to blame for Y. The people saying that are usually atheists or pretty close to atheistic in their thinking, and probably think religion is meaningless. I can sometimes see the logic in such statements, but it makes me wonder.
While I addressed some points above I want to go in extent to why many Muslims say this, and why their response is valid. Recall the phrase in statistical analysis, "correlation does not imply causation" classically expressed in logic as: (P & Q) ≠ (P → Q) ٧ (Q → P). While sometimes it looks like there is a correlation, we have to understand that even with a correlation (which there may or may not be) that causation should not be implied. If one wants to say Islam is the cause to the supposed correlation, they should support their view, otherwise it may be dismissed as ill speculation, especially when there is plenty of statistics, and data that argue against them.