I seem to have effective the same apparently insoluble "Assistants do not see" problem described by several other users.
The brief story is that the internal HD in my Mini died, but the Time Machine backups live happily on an external HD. However, with a replacement drive in the Mini running Mountain Lion (same version as on the dead drive), Migration Assistant would not find the backups on the TM drive, nor after wiping the new drive again (not like there was anything I wanted there) and going through Internet Recovery (which took me back to Lion) would Setup Assistant finf the the backups. In both cases, it would reach the "looking for other computers stage" (though, yes, I chose the right options to tell it I wanted to transfer from a external Time Machine disk) without ever finding the TM drive, which is attached directly to the Mini via Firewire and for which I can use the "Browse Other Backup Disks" option to go into TM and browse the backups there. And, yeah, I used Disk Utility to check out the TM disk; it's fine, so there should be no problem there. But, anyway ....
I'm now re-upgrading to Mountain Lion on the new internal drive, but I very much doubt anywhere in the process I will be able to use the Assistant to restore properly from the TM backups. I am using that, in the end, I will have to use a temporary Admin account to restore the old user folders and Applications folder from backup, and whatever I can find in the System and Library folders that looks like it won't mess things up too much. I guess if I get back the data in my old user folders -- iPhoto Libraries and stuff -- then at worst I'll have to reinstall some of the more finicky apps (Adobe stuff, MS stuff).
Still, it's tremendously annoying that although I can browse the old backups in TM, the Assistants won't do their job(s) of bringing things back relatively painlessly.
Considering that I am setting up a relatively virgin machine, how dreadful might it be to do things like do a "manual" restore of the backed-up System folders, etc. from the TM disk to the newly installed disk? Really _shouldn't_ that have the effect of restoring a lot of settings and app data? I mean ... at worst, the backups continue to live on the TM disk, so if anything got really weird on new internal disk, I could just start over by wiping it again and reinstalling Mountain Lion, etc. ... no?