Pile of nonsense. They are talking about Wigner functions, not probability, obviously.
In BEC, the temperatures are so low that electrons in the crystal lattice move very slowly. This increases their de Broglie wavelengths and thus the wave-like nature starts to dominate (over the particle nature). It causes a funny effect of the formation of so-called Cooper pair: electron which seem to attract each other (rather than repel because of Coulomb interaction). It happens when one electron and the positive ions of the crystal lattice attract, and this attraction distorts the crystal lattice - they ions sort of gather a bit closer to that electron. Such an accumulation of positive charge attracts another nearby electron (I guess that's the association with gravitational field the cited "team of experts" see). It doesn't mean that the electrons or the Coulomb interaction change their physical character in any way. Simply, the electrons are far enough from each other for the Coulomb interaction to be less valid than the lattice attraction.
We had experimental and theoretical lab investigating BEC at the institute. They wouldn't give me the degree if I didn't know the theory in detail (BCS derivation was obligatory)