How can the Gemara make the statement that the agent [delivering a get] investigates the matter very well so that he won't be compromised [by later having a husband contest the authenticity of the get]? ["Me'ikara meidak dayak velo atei le'or'u'ei nafshei"].
It seems a naive statement, as the rabbis were surely aware of cases with false witnesses.
The Gemara, according to Rabah, is not dealing with the possibility that the husband will say the Get is a forgery, or that he did not send the Shali'ach. In the case of a claim of forgery, we would indeed need Kiyum Shtaros, as you asked. In the case of a claim that the husband never appointed the Shali'ach, once the Get has been proven to be true, the Shali'ach is believed by virtue of the fact that he is holding the Get.
The Gemara, according to Rava, is basing itself on the fact that we assume that a Get is Kasher, due to the reasoning of Resh Lakish. Therefore, we believe the Shali'ach by virtue of the fact that he is holding the Get.