Yup, this is it. And you don't need to do it for every single backup. Before running the backup, do four coin flips. If they all end up heads (adjust the number of flips based on or how much time you can afford to spend on backup testing) you test the full recovery process of the impending backup.
Of course, it will depend on several parameters, but in my experience, doing a thorough test for a random subset of items is often more economical than a half-assed test of all items.
As a bonus, the random sampling will let you infer things about the totality of all items. (As opposed to any other scheme for selecting which items to test.) So once you've run 27 tests and only one failed, you know at least 85 % of your backups work. At 1/20th of the cost of testing them all, this is a good deal on information.