I failed to find anything in the video where the lip-smacker says the Z carries weak hypercharge. The Z does not carry weak hypercharge, or charge, just as the photon (its group-theoretic brother) doesn't. 

This is evident from [weak mixing](https://en.wikipedia.org/wiki/Weinberg_angle), since they, γ & Z, are a rearrangement of the [weak hypercharge](https://en.wikipedia.org/wiki/Weak_hypercharge) gauge field, *B*, and the $T_3$ one, $W^0$. Since these operators commute, the respective gauge fields are neutral w.r.t. them, and the eigenvalue of $W^0$ under $T_3$ is 0, while B is Abelian, so neutral, just as the phonon is such, under charge. So any combination thereof, like γ & Z, *also has to be neutral*! 

Of course, γ & Z do *couple* to Q and Q & Y respectively, as this is their function in the model.