I am just going off of what that Tennessee website had and the MOC catalog. The MOC does have the 17th/23rd Tenn's flag (Hardee Type), looking at it right now. War Department 144.
The MOC has War Department #147 "63rd Tennessee" listed as captured by the 11th New Hampshire.
I don't know who is right or wrong on this, but it is a confusing mess, when four different parties make different claims. It certainly is an error.