It all began in 1994 with Jason Patterson's original conspiracy theory. Although incomplete, it serves as a steping stone for the grand unified theory, hence deserving some sort of credit here:

1.The Conspiracy begins with Tori, after NIN has put out their first full-length album, Pretty Hate Machine (predestined reference to Tori?), sticking in her lyrics the words NINE INCH NAILS, in caps no less, in both her liner notes of her first full-length album, Little Earthquakes
2.{In Little Earthquakes,} Track 4 is named Precious Things (reference to Trent?)
3.Now on her second LP entitled Under the Pink Trent does backup vocals on the same Track number, this time entitled Past the Mission.
4.After this came out was soon the release of Reznor's second LP, The Downward Spiral (both titles refer to going BELOW something.. coincidence, I think not)
5.On his first single entitled March of the Pigs (pigs have red skin, Tori has red hair.. coincidence, I think not) there is a piano break that occurs twice in the song and Tori's songs are basically all based around the piano.
6.(not to mention that by the time of TDS, Trent and Tori had both put out a total of 2 LP's and one EP.)
7.In a track on TDS called The Becoming, Trent mentions a woman named Annie, which was Tori's nickname as a child. [ed. note: Annie was not Tori's nickname as a child, but this still may be a reference to her being reminiscent of "Little Orphan Annie", with red hair, etc.]
8.The rest of TDS is a lot more mellower than Broken, which was heavy, which shows a light influence (Tori possibly?).
9.Also, during the making of TDS in the Tate mansion, Tori visited Trent and tried to cook him dinner {the famous chicken dinner episode}.
10.Trent and Tori are now both on Atlantic Records. {at the time this original one was written}
11.Trent and Tori both have labels distributed by Atlantic Records.
12.As of now, they have both put out 2 singles off of their latest album.
13.Both refer to God and the divine in their lyrics.
14.Both use Apple Computers in their music-making. (note the Under the Pink liner notes, and interviews with Trent in Keyboard magazine March 1994).
15.The sum of the songs on both LP's are equal. (24)

16. Tori's song Cornflake Girl (Under the Pink), has the exact same hi-hat bassline as Trent's song Piggy (Downward Spiral). Who actually wrote it, we may never know.
17. In Tori's song Caught a Lite Sneeze (Boys for Pele), she makes prominent reference to NIN by including "Pretty Hate Machine" in the lyrics.
18. Both recorded (or own recording studios) in New Orleans, Lousiana.
19. A Christmas card was sent out to family and friends (exact date unsure) bearing a cartoon resemblance to Tori and Trent in a loving pose.
20. Both used dogs in the recordings of an album. Trent used Maise in Physical (Broken) and Tori used a runaway dog, Scrumpy, in the song Pretty Good Year (Under the Pink).
21. Both had classical training at an early age, and were groomed to be concert pianists.
22. Both have one deeply emotional and painfully introspective song in all their albums. Trent has Hurt, off of the Downward Spiral, and Tori has Me and a Gun, off of Little Earthquakes.
23. Trent's album the Downward Spiral refers heavily to pigs, and Tori's album Boys For Pele contains photos of her holding and breastfeeding a piglet.
24. The scene near the end of Trent's The Perfect Drug video (shot of the rooftop, with the boy looking on from the window), closely resembles the back cover of Tori's Boys for Pele album.
25. Tori's song Me and a Gun (Little Earthquakes) describes her rape experience, possibly using the word "gun" to refer to her rapist's penis, while Trent's song Big Man with a Gun (Downward Spiral) descriibes the act of rape, using the word "gun" to refer to a man's penis.
26. Both had one publicized romance with another musician. Trent, with Courtney Love, and Tori, with Eric Rosse.
27. Tori uses the word "nail" in her song Crucify (Little Earthquakes), as a representation of the nails driven into Christ on the cross, while the the name "Nine Inch Nails" may also have been used because of its connections to nailing Christ on the cross.
28. In the song "Tear in Your Hand" off of the "Little Earthquakes" album, Tori refers to Charles Manson in the lyric "I don't believe you're leaving 'cause me and Charles Manson like the same ice cream" and Trent recorded his album "The Downward Spiral" in Sharon Tate's house where she was killed by Charles Manson's brainwashed hippies. Submitted by BabsFarrow@worldnet.att.net
29.In Tori's "Spark" video, when she resufaces from underneath the river she brings her head up exactly the same way as Trent in "The Perfect Drug" video. Submitted by: Katt121@aol.com
30.Both released double albums on September 21, 1999.
31.Tori heavily used the word "Starfucker" in her song Professional Widow, and Trent released a song titled Starfuckers, Inc.

If you still aren't convinced, Angela Reid compiled a list of direct quotes from Tori Amos and Trent Reznor in a Q&A format and posted the whole bundle to rec.music.tori-amos one day. I've HTML-ized it for your viewing pleasure.