I had a quick look. Although I haven't found a specific error, as far as I can tell, he's not using the hypothesis of simple-connectivity anywhere in an essential way. Even though he posits this as a hypothesis in Prop. 5.6, the proof of this proposition works for any manifold with 2-sphere boundary (also, Prop. 4.4 works for any homology ball). Thus, in Step (4) of his proof of Prop. 5.8, when he refers to Prop. 5.6, this step is not making essential use of simple-connectivity.