I always had no luck getting them to overwinter and come back when I bought and planted them in the fall (even the ones that I made sure were labeled "hardy", as I know that many of the plants sold by florists and garden centers are not) -- have heard many complain about the same thing. But all the chrysanthemums that I have planted earlier in the year-- through mid summer-- have survived and come back year after year.
Ah, you've got me there. You're talking about the beautifully fall-colored mums which are sold in the autumn. You buy them (I do, at least, as an impulse purchase, not having thought it over usually,) and arrive home from the grocery store (or wherever) with the car full of mums!
Flowers, like mums, which do MOST of their flowering up to and even after frost may not be the best candidates for fall planting. If you wish to plant in the fall, it should not be a plant in the middle of a (maybe hormone-stimulated) flowering frenzy. It should be a relaxed, maybe even already slightly dormant plant. If you want chrysanthemums to return, happily and eagerly, year after year, you need to be respectful and polite that first year. For mums, that means 1.don't let them get freeze-thawed-freeze, 2.give them time to get established before the first frost (which may be out of synch with when they are sold as flowering plants), 3.make sure you have a cultivar that is hardy in your zone.
Good luck, and thanks for the extremely interesting question!