Well, I think even more than HFS or zFS, they use the MVS classic filesystem (datasets etc.) But that too is semi-hierarchical. (I say "semi" because to some extent the hierarchy is just a naming convention, but to some extent it's real – the initial qualifiers of a dataset name can be really hierarchical in that can select which catalog is used; and then of course PDS/PDSE members are an additional one-level hierarchy on the end.)

But you are right, there is nothing especially database-oriented about file lookup and naming on IBM mainframes. Record-oriented files and key-sequenced VSAM files (and once upon a time ISAM too) are database-oriented features, but they relate to file contents not file naming/lookup/etc.

I think the idea of catalogs is interesting, in that they permit a separation between the naming of datasets and the volumes they are stored upon. A dataset can be moved to another volume without changing the name used to access it. That is arguably more complex on Unix-like systems, since you need to muck around with symlinks or bind mounts to get the same effect.