Very briefly, it doesn't bother me. What makes the teachings authentic is not that they are the utterance of some god-like figure, but that they are in accord with the four seals of buddhism, and are teachings which bring about freedom when they are heard, thought about, meditated upon, and practiced.
It has been said that there are 84,000 doors to the dharma. This does not mean that there are 84,000 actual traditions, but that the buddhas teach in whatever way is needed to reach easch and every being. (Buddhists, as you may know, are not generally fans of extreme literalism.) All religions were taught by Buddhas. All of them. Reconciling this with the fact that religions often seem better at producing walking sermons and/or people who think that having memorizing more verses and being Doctrinally Correct has anything at all to do with a pure heart is what we buddhists call "pure view" - keeping in mind constantly that reality is actually free of faults, flaws, or stains of any sort.