isoPower Input-to-output dipole emissions
"Input-to-output dipole radiation is generated by driving a current source across a gap between ground planes"

So, you have 2 transformers that are placed across the isolation gap(literally above that gap). Usually whenever you have some sort of signal(current), its mirror image (that is usually on the ground wire/plane) will follow this signal. When this signal gets to the isolation gap, there is no path available for the mirror image, it will try to couple on to the other side, and that is what essentially causing the dipole emission. And this is why you're recommended to use stitching cap.

"Isolated power supplies, by their very nature, drive energy across gaps in ground planes"
No, if they are switched off, there will be no emissions. What they mean is that isolated power supplies are literally made to drive energy across gaps in ground plane.