I know it does not totally answer your request, but you totally can achieve that with Crashplan; and for free. Simply buy a NAS or equivalent, place it at your parents and install Crashplan on it.
It is not as perfect as a totally untied system like you want, but it is free and offsite :).
I am a happy customer of Crashplan for a while but other than that I have no ties there :).
In that case, you can buy a NAS for you, have them buy one for them, backup stuff on your own NAS and let the replication from your NAS to their NAS happen in the background.
Bonus: backups/restore/browsing are much faster, and you can more easily accommodate multiple people wanting to backup at the same place -- instead of one device at your place for each of your friend, it's only one at your place to which all your friend's NAS backup to.
I use Synology NAS, not with this setup, but I know they have the software to do exactly this.
Also, Crashplan has a "backup to friends" feature.
This is what I want (I know there are alternatives, but this is what I want):
A device that I buy, and can plug at least one hard drive in to. I give it some sort of passphrase. I then place it in a friend's house and connect it to their internet connection.
I can then access it remotely from my house. I can easily backup my stuff to it. My backups are encrypted, both over the wire and on the drive.
When my house burns down, I can drive over there and get all my photos and records and stuff, instantly.
I don't pay a monthly fee. I buy the device and then it is mine.
I know I can build this myself. I don't have time. If I could buy this I would.
It would be nice if it was easy to use the other way around, e.g. buy one for your parents and keep it at your house and automate their backups somehow.