quantum field theory - Equality of electric charges of all leptons

What does it precisely mean the often repeated statement that the electric charges of all leptons are the same.

Let's consider QED with two leptons: electron and muon. The interaction part of the bare lagrangian contains two electron-electron-photon and muon-muon-photon vertices with some coupling constants $e^{bare}_e$ and $e^{bare}_\mu$ respectively. After division of lagrangian into two parts: finite part and counterterms there are mentioned vertices in each part and the coupling constants in front of them are $e_e$, $e_\mu$ (finite/physical coupling constants), $\delta e_e$, $\delta e_\mu$ (become infinite when regularising parameter $\epsilon \rightarrow 0$; $\epsilon$ - deviation from dimension 4 in dimensional regularisation).

I suppose that the equality of charges of electron and muon means that 3-point vertex function $\Gamma^{(3)}$ at some fixed point $(p_1,p_2,p_3)$ has the same value for electron-electron-photon and muon-muon-photon vertex (is there any distinguished point?). That should mean that (at least in some renormalization scheme) $e_e=e_\mu$. However, in general, for finite positive $\epsilon$, $\delta e_e \neq \delta e_\mu$ because the masses of leptons are different and we need different counterterms.