Is this true in all cases?
One situation where a sheliaḥ must take responsibility for the action that he does is if it was a forbidden act. There the Talmudic principle “Ein sheliaḥ le-dvar aveirah” applies – that no one can appoint a messenger to commit a sinful act. The Gemara explains this by saying that the messenger’s true obligation is to follow the directions of God, not of another person: divrei ha-rav ve-divrei ha-talmid, divrei me shom’im!
The Talmud Yerushalmi presents a discussion on this point as to whether the concept of shelihut is true in all cases, and certain situations – like this one – are exceptions, or if we would ordinarily assume that a person cannot pass on responsibilities to another, and we need special teachings in order to permit shelihut to work. This discussion impacts on the question of a sheliaḥ le-dvar aveirah since according to the first approach we need to explain why shelihut will not work regarding a forbidden activity; according to the second approach it is obvious that we will not allow the creation of shelihut to do something forbidden.
Tosafot Ri”D argues that the Gemara does not mean to suggest that we would have thought that the messenger could have freed himself from responsibility for performing a forbidden act with the argument that he was only following orders. It is clear to us that an intelligent person must take responsibility for what he does. The discussion on this matter was solely to clarify whether the person who instructed the messenger should also be held accountable, since he was the one who instigated the action.