Just updated to 7.0.15, still got

2/10/2012 9:33:31 AM | Milkyway@Home | Master file download succeeded
2/10/2012 9:33:36 AM | Milkyway@Home | Sending scheduler request: Project initialization.
2/10/2012 9:33:36 AM | Milkyway@Home | Requesting new tasks for CPU and ATI
2/10/2012 9:33:37 AM | Milkyway@Home | Scheduler request completed: got 0 new tasks
2/10/2012 9:33:37 AM | Milkyway@Home | No tasks sent
2/10/2012 9:33:37 AM | Milkyway@Home | Message from server: GPU lacks necessary double precision extension

My GPU is AMD Radeon HD6970 (Cayman), drivers are updated (12.1).
Milkyway@Home admins keep telling that they check correctly in their scheduler, in fact for some people it is working. Yet on my computer it does not work. They told me that my BOINC Manager isn't reporting all the cl extensions to the server: cl_khr_fp64 or cl_amd_fp64 is required for that app and it's missing in the info my boinc manager reports back.
If I query clinfo locally I can say that I have cl_amd_fp64 (cl_khr_fp64 still not available, should be in one of the next catalyst release, but at least I have one of them).

Sorry, they found a bug in their code.
Now it's working, so the bug is not on your side!