Nine Inch Nails have never explicitly stated that they are members of the industrial genre.
For example Pretty Hate Machine (1989) was much more of a synth pop album with elements of Industrial mixed in- although he admits to 'Down in it" being heavily inspired by Skinny Puppy- Dig It. Skinny Puppy being a Canadian Industrial group noted for their abstract and shocking music. Pretty Hate Machine being closer to Cabaret Voltaire's style of Industrial, much more computer generated beats and loops, using samples but not straying too much into Rock.
The Industrial influences of Ministry come across far more in the next release 'Broken', which was an overall much heavier album which clearly draws on from ministry's heavier vision of the industrial genre, with songs such as 'Happiness In Slavery' and 'Wish'. The next Release, 1994's, The Downward Spiral draws into the industrial genre heavily, the computer generated music fused with the instruments it's far more of a 'typical' Industrial record dealing with the traditional Industrial themes of the break down of society and what that'd cause0 a theme strong throughout every song on the album. This is where many say that Nine Inch Nails really came into the genre and it inspired much of the Industrial music available now.
The Fragile was in many ways much more of an album that's in many ways quieter than prior releases, also much longer and in almost a contrast with the Downward spiral, its a much more personal based album.
With_teeth is a much more mainstream Rock album, its very punchy in line with a more modern approach to industrial music and the industrial design. It's interesting to note that around this time Skinny Puppy launched back into action.
Year Zero is where the real politics of NiN comes out, highly critical of the Bush administration of America (as many musicians where). It details a near future society where the American government was too powerful and merged with the church- it accompanied a ARG (alternate reality game).