How can I trust Time Machine again?
I reformatted my MacBook Pro (Mid 2010) and did a clean install of Mavericks. Now it won’t recognise my Time Machine backup in either Migration Assistant or Recovery ( ç+r). It can see all the backups in Finder. I’ve installed an earlier backup from Carbon Copy Cloner, but I have no luck with Time Machine. I also use Time Machine for my iMac and need to know if this is a regular problem as I now worry about backing up my Macs. Bob Collins
Your backup is fine, you just used the wrong tool to restore it. Migration Assistant is designed to move a user account (and its data) from one Mac to another. It creates a new user account with the same name and then copies data from the most recent Time Machine backup.
The trouble is OS X has a hidden number (called the UID) that it uses to distinguish accounts. The first one created on a new Mac is numbered 501 and it counts up from there. When you first start a new (or cleaned down) Mac, the Setup Assistant asks you if you want to restore from Time Machine. If you do it then and there, the data is copied to UID 501 and everything works fine. Otherwise, a new account with UID 501 is created, so when you run Migration Assistant later, UID 501 is already taken and it creates UID 502. Though the account name might match the backup, the different UID stops you restoring.
There’s a way to shuffle the 502 account to 501, but it’s pretty complicated. The simplest way out of your predicament is to reformat once more, but this time opt to restore from Time Machine during the Setup Assistant.