There's goth music, and there's music that goths tend to listen to quite a bit. NIN are the latter, and I'd say that is to be expected considering a) their influences, particularly Joy Division, Gary Numan, Bowie, Bauhaus, Love & Rockets, Ministry (again, most of those fall squarely into the second category), and b) the strong association between goth and industrial /industrial rock during the 80's- 90s.

The Pumpkins are definitely more directly rooted in goth music, to varying extents through their career. Much of the pre-Gish material was very Cure influenced.

Of course The Cure are now considered a classic 'goth rock' band, but their works are far too varied to apply that moniker to them as a whole. And of course basically anyone who that term was applied to distanced themselves from it