1. The covenant may only exist on Nirn, thus when the Amulet is outside of Nirn (specifically in Oblivion), it is not bound by the Alessian covenant, so anyone could wear it.
2. Mankar Camoran happens to be aided by Mehrunes Dagon. Is it possible that Dagon gave Camoran the power to wear it?
3. It could be an illusion - making the champion THINK that Camoran could actually wear it.
4. Could it be possible that Akatosh allowed Camoran to steal it and give him the power to wear it and in turn make the champion kill him to get the Amulet back? In consideration of the fact that Camoran was considerably against Akatosh, and Akatosh against Camoran, that could make sense. Also, it could be part of Akatosh's plan to dissolve the Alessian covenant so he could attack Skyrim in the pursuing years as Alduin.
Just a few speculations, feel free to correct me anywhere I'm wrong.