I have done Hartree-Fock calculations on a single He atom and now I tried to check numerically if the electron density fulfills the Kato theorem. It apparently doesn't. Instead I obtain a cusp corresponding to an effective charge of about $1.76$. That looks suspiciously like an effect due to the effective shielding exerted from the second electron. The Slater rules would suggest to expect an effective shielding of $0.3$ which is not that far away.
Also by theory one would expect such an effect, as HF is a "mean-field theory" treating the electrons seeing the mean potentials from the other electrons. Possibly one could even derive the exact deviation?