Yes, except that this thread is not about damaged machines. It's about data security.
True, but if you have a "good" backup, and prepare properly, you can reboot your machine from an "external source", use Disk Utility
there to Erase and Format (and if necessary, partition) your internal drive, do a fresh, "virgin" installation of the Mac OS you are using, and then use Migration Assistant to "migrate"/copy needed "stuff" from your backup. Reboot your machine, and you are back in business.
If the backup is "infected" also, then yes, that will not work. As long as your internal HDD is OK (from a mechanical perspective), you could still boot your machine externally, use Disk Utility to erase and Format the drive, and then do a clean, "virgin" installation of the OS. Reboot your machine, and then you would need to add any third party applications one by one. I actually suspect that if the backup is bad, and the drive is OK, that is what the folks at the Apple Store would do.