Who says she would have?
I actually do think she would have, but I haven't heard anyone actually make the case. Here's what I think:
[1] As BRTD pointed out, Bush was a good candidate for the region compared to both McCain and Romney. Romney was actually a terrible candidate for the region, but not as bad as Obama.
[2] Kerry was a terrible candidate for the region. Massachusetts, rich, liberal, and then there was his wife. Although he did help himself with John Edwards, it's the top of the ticket that counts.
[3] Gore wasn't really a southerner anymore by 2000. He was a DC'er. When you're away from your home state for 8 years, join an economically (classically) liberal administration that emphasizes the "New Economy", shift to the left, and take up causes like environmentalism, you're no longer Tennessee's or Appalachia's home boy. I remember when Gore had to move his HQ from D.C. to Tennessee in the middle of the campaign and it became another emblem of his supposed insincerity. Bush was a great candidate for the south and Appalachia, and that's what did it. But Gore did have enough vestiges of southern in him to make Florida as close as it was. He still did light years better than Barack Obama in Appalachia.
But my main case is based on
the polls in 2008. For instance, our polling average shows
Clinton was lagging McCain by just 5 points in Kentucky at the time she lost her nomination battle. At the same time,
Obama was losing the state by over 30 points. Three polls taken in West Virginia showed
Clinton leading by 3 points in May while
Obama was losing by 10 points. In Arkansas Clinton had a
2 point lead in Arkansas, when Obama was losing by
25 points. Missouri is closer, but shows the same pattern. In early May,
Clinton and McCain were tied, whereas Obama was
slightly behind, although he closed the gap after the nomination. But for instance, if you look at the Survey USA poll taken May 18, Clinton was up 2 and Obama was down 3 in the same poll. In the May 6 Rasmussen poll, McCain was up 6 on Obama and only up 2 on Clinton. In the April 13 Survey USA, McCain was up 8 on Obama but down 1 to Clinton, and so on. Finally, there is Tennessee. The early April 2008 polls show
McCain opening a 10 point lead on Clinton, (partially based on an extremely suspect polling firm, Ayres McHenry) but he was leading Obama
by at least 15 points. For instance, on the April 3 Rasmussen (the last GE poll to include both candidates), McCain led Clinton by 14 points, but he led Obama by an astonishing 27 points. The February 28 SurveyUSA poll (the second to last poll excluding Ayres McHenry), Clinton was tied with McCain. Obama was down 16 points in the same poll. Further, a quick glance at the chart shows Tennessee voters considered Clinton much more consistently than Obama- she actually led the polls in late 2007. Obama never came close.
Finally, there is the fact that the virtually singular, herculean Republican swing in Appalachia the heavily Democratic wave year of 2008 was too much to be explained as the product of long-running, secular factors. These are states (with the exception of Missouri) that were Clinton's biggest sources of margins in the primary by far. And in 2006 many of these areas sent blue dog conservadems to Congress and state capitols by huge margins. All indications point to 'personal' (i.e. personal to the Dem candidate) factors for the Republican Presidential ticket doing so well in Appalachia.
Given the fact that the May polls were taken before Lehman Bros. & the national popular vote was roughly tied at the time, I believe Clinton could have easily carried Arkansas, Tennessee, Kentucky, West Virginia, and Missouri as her husband did in 1996.