No, it was the shed skin of the original Dragon, created when it split into Reshiram and Zekrom.
From bulbapedia: "Drayden tells the player character that when the original dragon split into Reshiram and Zekrom, a third dragon was "created", or "leftover": Kyurem." We also have the Pokedex entry stating that truth and ideals are missing from it.
This makes a lot more sense seeing as the DNA Splicers work with Kyurem to fuse it with Reshiram/Zekrom. If Kyurem was to have no relation to the original Dragon, it would likely be too far away a relation to Reshiram/Zekrom in order for it to work. And of further note is that DNA Splicers was created around the time of Dragonspiral Tower, which was used to house one of the Dragon stones.