Antenna diodes work even though their breakdown is greater than the MOS gates, because the same plasma processes that deposit the charge, also throw off enough UV / soft X-rays that the diodes become photoconductive. Likewise the S/D diodes and well-substrate diodes become shunts despite high normal breakdown voltage.
Another fortunate development in newer nodes is that all gate oxides, or at least the non-I/O core, have so much tunneling current normally that antenna charging may not cause damage (the old trap-hopping percolation process was more damaging / drift-causing; tunneling does not interact with the intervening region, by definition).