The K'tzos Ha'choshen (182) quotes the Tosafos Ri"d who asks why do we not allow the concept of שלוחו של אדם כמותו by mitzvos such as tefillin and sitting in a succah? The Tosafos Ri"d seems to say very simply that a mitzvah must always be done by the individual himself, with the exception of marriage and divorce since the actual חלות of the kiddushin/gerushin is for the sender. The Ketzos asks, that if this is true, why would we need a special source to say אין שליח לדבר עבירה, which implies that without a special limud, we would assume that reuven can be responsible for an act of aveira done by shimon. Even without a special source, we should never be able to trace the aveira of shimon back to reuven, just as we can't trace the mitzvah act of shimon back to reuven? The Ketzos has an entirely different approach to this question (i mentioned it in my sefer nasiach b'chukecha pg. 113).
The Ohr Sameiach (shlichus 1:1) comes to explain the Tosafos Ri"d. There are certain mitzvos where the intent of the Torah is that everyone should do a particular act. For example the Torah wants every individual to wear tefillin, eat matzah and sit in a succah, so it is impossible to say that when my shliach does these acts, it is as if i did it myself, since that would undermine the entire intent of the Torah. If one were able to appoint an agent for these activities, one person could eat matzah for the rest of the world, which surely undermines the intent of the Torah. However, when the intent of the Torah is that the action should be attributed to me, such as korban pesach where the Torah isn't interested in my shechita, rather my association with the korban pesach, a shliach can do it for me. Similarly by kiddushin, the torah wants everyone having a wife, but there is not concerned that everyone should do the act of kiddushin himself, and it can therefore be done by a shliach.
Based on this approach, when it comes to stealing, killing, adultery.... the torah demands that no one do these acts, to prevent the result. Since the intent of the Torah is not merely to refrain from the act, but to prevent the result, these aveiros are similar to kiddushin and gittin where the main purpose is the result, not the act. Just as the Torah says that Reuven can appoint shimon to do kiddushin since primary issue is the result which can be attributed back to the sender. Similarly the Torah forbids stealing and killing because of the result, so when Reuven causes someone to be killed or stolen from by appointing Shimon to do it, the act can be attributed back to the one who causes the result, Reuven. Therefore, without a special pasuk teaching that you can't have a shliach for aveira, one would think that Reuven can be held accountable when Shimon does these acts for him.