Equality of regular and generic non-tangential singular sets

Let $\mu$ be the measure under consideration, and let $\mathcal{S}_{nt}^{reg}(\mu)$ and $\mathcal{S}_{nt}^{gen}(\mu)$ denote the regular and generic parts of its non-tangential singular set, respectively. Equality conjecture.

$$\mathcal{S}_{nt}^{reg}(\mu)=\mathcal{S}_{nt}^{gen}(\mu).$$

This claim is resolved: the source states that it is proved in Lemma cited in the status evidence, which constructs a measure with a non-meagre singular set.