I discuss string theory on AdS3xS3xT4 in the tensionless limit, with one unit of NS-NS flux. This theory is conjectured to be dual to the symmetric product orbifold CFT. I show how to compute the full string partition function on various locally AdS3 backgrounds, such as thermal AdS3, the BTZ black and conical defects, and find that it is independent of the actual background, but only depends on the boundary geometry. Consequently, reproducing the boundary partition function does not require a sum over bulk geometries, but rather agrees with the string partition function on any bulk geometry with the appropriate boundary. I argue that the same mechanism could ensure factorization of the bulk partition function when geometries with disconnected boundaries are considered.