I spent some time checking into things, and here's what appears to be happening:
1. I do get an IPv6 address from Time-Warner... and it appears to be legit. (It's not the link-local address; it starts with 2605:e000, which is in the Time-Warner block)
2. But... it appears to be non-routable from the general internet. I think this is Time-Warner's fault. But maybe it's my router. I am not sure. Traceroute from http://4or6.com/traceroute?l=en gives me this. (I attempted to obfuscate my real address with XXXX)
#traceroute 2605:e000:xxxx
traceroute to 2605:e000:xxxx (2605:e000:xxxx), 30 hops max, 80 byte packets
1 2607:f2f8:1600::1 (2607:f2f8:1600::1) 1.653 ms 1.597 ms 1.583 ms
2 2001:504:13::1a (2001:504:13::1a) 11.753 ms 11.746 ms 11.732 ms
3 twcable-backbone-as7843.10gigabitethernet17.switch2.lax2.he.net (2001:470:0:2bf::2) 2.618 ms 2.610 ms 2.599 ms
4 2001:1998:0:4::11d (2001:1998:0:4::11d) 3.956 ms 2001:1998:0:4::11b (2001:1998:0:4::11b) 3.477 ms 2001:1998:0:4::11d (2001:1998:0:4::11d) 5.512 ms
5 2001:1998:0:8::83 (2001:1998:0:8::83) 4.090 ms 5.784 ms 2001:1998:0:8::87 (2001:1998:0:8::87) 6.542 ms
6 2605:e000:0:4::41 (2605:e000:0:4::41) 6.753 ms 5.032 ms 5.011 ms
7 2605:e000:0:4::5:7f (2605:e000:0:4::5:7f) 6.859 ms 7.042 ms 7.128 ms
8 * * *
3. Since a recent firmware upgrade, my router detects this problem, and sometimes (but not always) decides to set up a 6to4 tunnel. I am not sure how this works, exactly.
4a. If the router does set up the 6to4 tunnel, I do have IPv6, but as organsnyder says, since 6to4 tunnels suck, the OS prefers to use ipv4.
4b. If the router does not set up the 6to4 tunnel, I have a completely non-functional IPv6.
Oh well, maybe next year.