= Solution
Corrections quadratic in the cubic-anisotropy coupling use two $\lambda_0\sum_a\phi_a^4$ vertices joined by two fast propagators. Because all four legs at each anisotropic vertex carry the same component index, the internal propagators force the two vertices to have that same index. The resulting one-loop bubble renormalizes the anisotropic tensor $\sum_a\phi_a^4$, hence $\lambda$, but does not generate the distinct-index structure in $(\boldsymbol\phi^2)^2$ needed for a correction to $g$. There is no freely summed closed component index, so the diagram is not proportional to $N$.
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