Richard Rackham suggests the following in his discussion of the Jerusalem Council (Acts 15:1–29).
"We now come to a narrative which bears strong testimony to the fidelity of S. Luke. This is indeed incidentally confirmed by the relation of S. Paul to S. Barnabas: at Jerusalem, and in official records, Barnabas stands first (verses 12 and 25), but where S. Luke narrates, or gives his version of the record, he slips into the usual Paul and Barnabas (verse 22: cp. 2 and 35). But the chief evidence is afforded by the speeches. These are of course only brief notes of what was actually said, written out afterwards by S. Luke; and yet in these few verses the characteristic attitudes and phraseology of the speakers unconsciously assert themselves."
Richard Belward Rackham, The Acts of the Apostles: An Exposition (London: Methuen & Co., 1901), 247
While I am a believer in Luke’s fidelity, I am not sure I am convinced that order of names is all that determinative.