Well, sort of, yeah you're mostly incorrect. While raid 10 gives you an effective raid of raids, it's still made of active disks with too much in common with each other.
What if the power supply releases its magic smoke and takes most of the hardware it powered with it? What if your wife accidentally deletes your family photos directory? Kid spills water inside the cabinet? FSM smites you with a noodly appendage?
While your data is very redundantly stored with raid 10, you'd be much better off buying a monster HDD (or two) and making monthly / weekly / whatever snapshots. Let's face it, your home network data probably doesn't change that often and a decent raid 5 may well be overkill for uptime as well as speed. If you're really gonzo, make a yearly snapshot and send the disk (well labeled with your name and the word archive!) to a buddy where it can gather dust safe from anything including the destruction of your house.