I always thought it was either because the system was capable of supporting a disk file system or because parts of the operating system are swapped to disk.
If DOS means the latter, was there a non-disk PC perating system -- one which is always fully resident? Would the BIOS qualify?
It means the system is capable of supporting disks, including a file system.
It doesn’t mean that parts of the operating system are swapped to disk. Since you’re referring to PC operating systems specifically, DOS implementations on the PC can reload parts of themselves from disk (the command interpreter; see How does the command.com shell work with MS-DOS? and TSRs at top of memory conflicting with COMMAND.COM for details on MS-DOS specifically), but they don’t swap anything out to disk.
There were fully resident versions of DOS; for example HP’s DOS-based palmtops had MS-DOS in ROM. DOS in ROM runs directly from ROM, leaving RAM for programs. The original IBM PC could run BASIC from ROM (Cassette BASIC), and would boot to that if no bootable disk was present.
