Thanks to the many different people who emailed me about this. Tori Amos was mentioned on the 'Hot Mamas' episode of VH1 All Access which first broadcast on August 11, 2003. The show will be repeated on these dates/times:

Friday, August 15, 2003 - 10:00PM ET
Sunday, August 17, 2003 - 11:00PM ET
Wednesday, August 20, 2003 - 3:00PM ET
Tuesday, August 26, 2003 - 11:00PM ET
Wednesday, August 27, 2003 - 10:00PM ET
Thursday, August 28, 2003 - 4:00PM ET
Sunday, August 31, 2003 - 3:00PM ET

More Details

The short Tori segment was part of section of the show about an interior designer named Wendy Bellisimo, who mentioned a blanket that Tori fell in love with and decided to do Tash's whole crib set around it. They showed parts of Tori's Strange Little Girls video as well. You can find a video of the designer talking about it at VH1.com. The TV show version of this video shows shots of Tori while the designer is talking.