They will if the Corporate HQ for the US is in a state with such laws. Either that or they risk a lawsuit...and yes, I pretty sure he won't, but if their legal team says they're at risk. They'll want to minimize that as much as possible.

EDIT:

I doubt people will listen to this...but.

Please do not Dox her in the sense of releasing all the information you can find.

Release only the information type she released of this man.
--This means you release photos of the house she lives at, license plate (think that was there). You essentially are mirroring exactly what she posted...only with her name.
...I would not be surprised if she turned around and cried foul