A recent paper suggests that MOND would better explain the difference in the distribution of rotation curves inside versus at the outer edges of galaxies. It would be due to the External Field Effect (EFE) encounter with MOND for galaxies in a uniform external field due to surrounding systems. ΛCDM, based on General Relativity (GR), respects the (strong) equivalence principle. Accordingly, for ΛCDM, such differences are not directly explainable. As the observed difference is argued to be statistically significant, something still to be confirmed, it could be a convincing argument in favor of MOND.The paper explains how the multi-fold dark matter effects explain qualitatively the observed differences: inner entanglement is more disrupted by the rest of the galaxy content, before creating a halo effect. With this we can argue that MOND is not necessarily the only answer to the observations. In previous papers, we argued that the multi-fold theory at large enough scale recovers GR, and that it is compatible with the equivalence principle. The paper therefore explains that these can be multi-fold gravity results. The multi-fold dark matter effects result from entangled real systems, which are extra contribution to gravity, which results only from virtual particles. There are therefore no inconsistencies: the equivalence principle can be respected while rotation differences may exist. To that effect, we show that while multi-fold gravity follows the (strong) equivalence principle, multi-fold dark matter effects can bring in an EFE effect without any contradiction.