I live in the urban part of Seattle. The moon was full the other night and I definitely noticed. With that being said, the effect is not as noticeable than in areas with no light pollution.
Right, I would definitely expect it to be a lower impact. I've spent nights in rural Wyoming and the full moon makes a huge difference there compared to my suburb, and I'd assume a similar effect going from suburb to downtown.
The weird thing about this piece is that the data explicitly shows that the effect size is much smaller for the urban population than for the rural, which suggests that the mechanism that triggers it is duller for them but not absent.
Going from "it's Seattle" to "so the moon is invisible" to "so maybe humans can sense gravity" was a set of violent enough leaps of logic to leave my head spinning.