An electron orbital overlaps with the nucleus, though; any bound electron can in a very real sense be said to exist partly inside the nucleus all the time. But electron–nucleon physics don't care. In particular the electron does not feel the residual strong force. The situation is different with a bound antiproton, however. If the antiproton wavefunction ends up sufficiently overlapping with the wavefunction of one of the nuclear protons, they will annihilate.
These electron quantum rules don't work the same for an antiproton, which is 1800X more massive than an electron. There's probably some other factors, like the antiproton can get close enough to the nucleus for strong force effects etc.