I find it helpful to distinguish between Agile, the thing that is waterfall in new terminology, and agile, the philosophy of how to flexibly adapt the way of building software to the lay of the land. You "do" Agile, or you "are" agile, never both.

The litmus test is quite simple: are sprints planned more than one sprint ahead? If an organization has a schedule where they map work to sprints months in advance, they are doing Agile. If they just have a backlog and the only planning they do is in preparation of the next sprint, they stand a chance of being agile.