Step 1: Identify Sibson's fascia. It is the suprapleural membrane, a thickening of connective tissue that forms a dome over the apex (cupola) of each lung, separating the thoracic inlet structures from the neck.
Step 2: Note its true attachments. It attaches to the internal (inner) border of the FIRST rib and to the transverse process of the C7 vertebra. It is derived from the scalenus minimus (a slip related to scalenus anterior/medius) and gives protection to the lung apex.
Step 3: Evaluate each option. Covering the apex of the lung (b), being a derivative associated with the scalene muscle (c), and having subclavian vessels cross over it (d) are all correct. The statement that it attaches to the inner border of the SECOND rib (a) is false - the attachment is to the FIRST rib.
Step 4: Therefore the INCORRECT statement is option a, which is the requested answer.