Missing backups from Time Machine
I suspect based on the comments, that Mike Meyers has a point, in that you are only seeing  MobileBackups, and that tmutil is simply showing you pointers (or logs) to the Time Machine backups on the linux server. For some reason the actually backup on the drive is not readable by Time Machine. I suggest dumping the network drive to an external, OS Extended Journaled hard drive and see if you can point Time Machine to that.