I still haven't got hold of Zinn-Justin's book mentioned in the comment, but here is a plausible/consistent interpretation of what that statement might mean. Generally one has to distinguish two kinds of RG flows and thus two kinds of beta functions, one is about pushing the UV cutoff to infinity and defining a QFT (i.e. UV completion), the other is about coarse graining the theory to gain IR information (Wilson-Kandanoff-Fisher). The former slides a unphysical cutoff scale $\Lambda$ and the latter slides a physical probing/experimental scale $\mu$, and the beta functions are respectively denoted by $\beta_\text{UV}(g_\text{bare}(\Lambda))$ and $\beta_\text{Wilson}(g_\text{ren}(\mu))$.

The two are perturbatively very similar when one has dimensionless couplings ( see the "Update" section of this answer. In fact Wilson and Kogut only called the latter kind "RG trajectories", and the former "canonical curves"), but no a priori relation exists for general couplings.

For super-renomalizable theories, UV-finiteness require $g_\text{bare}(\Lambda)=g_0+o(1)$ (small o notation, with respect to $\Lambda$, and $g_0$ is independent of $\Lambda$), so the beta function in this sense must be 0 near $\Lambda=\infty$, and it might be this beta function that Zinn-Justin was talking about. On the other hand, since the coupling is dimensionful, we can almost be sure that the theory is not scale invariant hence the beta function in the sense of Wilson is not 0.