Restoring iPhone from Backup
I got my iPhone replaced yesterday. I didn't have a recent backup on iCloud so the genius told me that I could just back it up to my MacBook Pro, even though it is not synced to my MacBook Pro. I did and I came home to restore it. Restoring it from the Backup on the MacBook Pro doesn't restore the apps and the app layout like he promised me it would. Was he wrong? Can a backup to a non-syncing computer restore everything back to the phone, including apps?
MacBook Pro, Mac OS X (10.7.2)