I had a complete TM back up. Harddrive connected to an airport extreme, backing up daily. So when my laptop goes awol and. I get a new one, the TM backup is not visible on the new mac. Hours on the phone with apple support, eventually on to a senior advisor and my backup was nearly erased following apple support advice!
I managed to force the backup on to the laptop and it took 24hrs to load. 3 weeks later the logicboard on that machine crashes so apple replaces it and I'm back to the exact same problem trying to load the backup. I gave up and ended up copying and pasting what I needed to pull off it.
So if apple doesn't know how to deal with it, it's pretty bad. I was also told that setting up a backup system via an extreme is a bad idea.
I'm not using time machine at all now.
(By the way, i am a trained network engineer and worked in IT. i'm not totally lost when it comes to computers, PC or Mac.)