= Solution
Begin with the same ammine <deprotonation> and amido-assisted weakening/cleavage of the Co-S bond, but now SCN$^-$ is already beside the metal. A \b[solvent-caged pair] of five-coordinate cobalt amido species and the departing thiocyanate can reorient and recombine through nitrogen before the ligand diffuses into bulk solution. Reprotonation restores the five ammines and gives A.
Thus the essential sequence is
$$
\mathrm{Co{-}SCN\xrightarrow[\text{ammine deprotonation}]{OH^-}
\{Co_{\rm amido}\cdots SCN^-\}_{cage}
\longrightarrow Co{-}NCS}.
$$
<Water> capture competes to give Co-OH, but rapid internal return of the already associated ligand accounts for the high yield of A. The slower entry into the reactive conjugate-base/dissociation sequence is followed by faster reorientation, capture and proton transfer. This is <linkage isomerization>, not oxidation or reduction of cobalt.
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