If you can't automatically restore, it's because you've lost data. There is a huge variance on the data value and difficulty or recreating it, but a backup should let you clearly and unambiguously recreate whatever system you are backing up.
Not exactly. There are a lot of possible scenarios where the data isn't last, but can't be automatically restored. A broken tape for example isn't lost data, but it will be a big pain to recover from. If the data isn't properly indexed you will have a big problem figuring out what file goes to what machine, but the data can still be there.
You will have a hard time to find a backup program that doesn't have a good and tested restore procedure. However that doesn't mean it works in your particular edge cases.
Even if the backups would work perfectly, this forced downtime might the best time to apply some change that your admins have known should be done for a while but couldn't afford the downtime. (you couldn't do a schema update, but there are some smaller config changes that still require taking the master database done for a bit)
