Backing up Health app data to iCloud

There seems to be a lot of misinformation on the Internet and even from Apple Store employees about backing up data or the Health app to iCloud.

It turns out you may backup health app data to iCloud if you opt to use an encrypted iCloud backup.

The option to encrypt the backup can be enabled in iTunes, but how it is placed would lead you to believe that it is only possible when you backup on the computer (that's not the case). Check the box, start the backup, choose a password - it will be required when you try to restore that backup.