A fairing is not part of the wing, that is correct. It also could be a cousin, the fairing under the Horizontal Stabilizer. From its shape and the contour of the "leading edge" negative, it too could have been oriented as above.
If near the HS, it could be associated with the "trimmable" Horizontal Stabilizer piece found as described by BEA. The "cutout" (negative) in the Aluminum is hard to judge, but I do believe it was near an airfoil.