1) During the Oblivion crisis Martin determines that to open a portal to Mankor Camoran's paradise, he needs the blood of a divine and asks the player to get a piece of Tiber Septim's armor. Every other item he asks for (Grand Weykland stone, Daedric artifact, and Great Sigil stone) is verified as being "really" what they are. Therefore, since Martin IS able to open a portal to paradise using Tiber Septim's armor, that seems to confirm that it really is a divine artifact.
2) The second piece of evidence is rather indirect, but may explain the Thalmor's motivations. According to the Old Ways, gods are really just very powerful ancestors that many people worship. The more people that worship them, the more powerful they become. The less people that worship them, the less powerfull they become. This actually fits with Elven understanding of creation where the gods, the aedra, are "our ancestors" vs the daedra who are "not our ancestors." If this interpretation of divinity is correct, then the fact that many people worship Talos is by itself enough to make him into a god. Going by the Od Ways, then, the way to un-do Talos's divinity is to get people to stop worshiping him. If the Thalmor can succeed at that, then they can deprive Talos of his divinity. This would be especially important to the Thalmor since Talos was a man and therefore not an ancestor of the elves, perhaps meaning their connection to this god is attenuated compared to their connection to the other gods.