A (Unix) file system is a hierarchical database for unstructured untyped data. The BeFS is more like a metadata-addressable graph of semi-structured data. The VMS filesystem is a hierarchical database for semi-structured versioned data. The OS/400 filesystem is actually pretty close to SQL in its semantics. Different filesystems are very different!
NoSQL is a movement that advocates choosing the best-fitting database technology for your data model. (NoSQL == Not Only SQL)
If you have tree-shaped unstructured data, then storing it in the (Unix) filesystem definitely fits the goals of the NoSQL movement. If your data however is relational, then choosing the filesystem is actually exactly the opposite of NoSQL: remember, NoSQL means choosing the best-fitting database technology for your data model, and if your data is relational, then that model is SQL.