If an author declines authorship, may her co-authors publish without her?
It seems to me that if authors B and C write in the acknowledgment section that the contribution of person A was sufficiently important that they think A should be listed as an author but that A declined and especially if authors B and C provide a description of the reasons leading to A's refusal which is satisfying to A, in other words if B and C report accurately what has been happening, then no one is behaving unethically.

For a real life example, one can look at the acknowledgment section of S.Bloch and K.Kato's work on p-adic étale cohomology, the third author being in that case O.Gabber and the reason invoked (if I recall correctly) being that Gabber did not think the work was ready for publication (I'm unable to track the precise reference at the moment, it is not Bloch and Kato's article at the IHES in 1986).

UPDATE: Because I haven't been able to track the reference of Bloch-Kato, let me point out Beilinson-Bernstein-Deligne which starts with


  Il avait d'abord été prévu que O.Gabber soit coauteur du présent article. Il a préféré s'en abstenir, pour ne pas être coresponsable des erreurs ou imprécisions qui s'y trouvent. Il n'en est pas moins responsable de bien des idées que nous exploitons et le lecteur lui est redevable de nombreuses critiques qui, nous l'espérons, ont permis d'améliorer le manuscrit.


which roughly translates as 


  It was first planned that O.Gabber would be coauthor of the present article. He chose to abstain, so as not to share the responsibility of the mistakes or imprecisions to be found in it. He is nonetheless responsible of many an idea we exploit here and the reader owes him numerous criticisms which, we hope, allowed for improvements of the manuscript.