The potting mix should cover the roots, leaving the stems (and much of the crown) exposed. Your instincts are exactly right.

I recently re-potted my spider plants. Well, I split one of my spider plants into four. Here's a thread where I posted pictures of one of them.
http://forums2.gardenweb.com/forums/load/houseplt/msg0910550617315.html?6

The second post has a picture showing a new shoot coming up next to a re-potted spider plant. Off to the right is one of the leaves coming up from under the peat-pudding potting medium. The lowest leaves are that deep under the soil, but the plant is producing vigorous new growth, both the new shoot and up at the top. There is one dead leaf in the foreground, but I think it was damaged as I hacked the plant apart.

Here is a link that might be useful:

Thanks! They definitely have it sitting deeper in the pot than that. No wonder the last one rotted and died on me so quickly.
I'll repot it a bit shallower, and hope it makes it! It actually doesn't look too bad, so I think it has a chance.