Are Acts 15:36-41 and Gal 2:11-13 Describing the Same Event?

Will Willimon in his Interpretation commentary on Acts states,

The reasons that Luke gives for the breakup of the Paul and Barnabas team does not square with Paul's version in Galataians 2:11-13.  Paul's own assertion that he had doctrinal differences does not fit in with Luke's purposes (p133)

But it is surely incorrect to conflate the two events.  Paul gives no hint in Galatians that his disagreement with Peter led to a schism between him and Barnabas, but only expresses surprise that Barnabas should be led astray by Peter's actions (Gal 2:13).  Which statement surely evinces a high regard for Barnabas.  Rather, in this instance I think the criterion of embarrassment suggests that this episode in Acts does not show Paul in the best light, especially given the fact that Barnabas' trust in Mark is eventually proven correct (Col 4:10, Phil 24) and Paul and Barnabas later reconcile (1 Cor 9:6, Col 4:10), and is therefore a reliable account of the reason for the division. 

Is anyone aware of anything that would support Willimon's assertion?  Is there something I have missed?  It seems rather cut and dried to me.  let me know what you think :-)