I'm an older 8-bit computer geek (or nerd if you prefer) and I still own and use real C64 computers. CBM DOS made in 1983 (or earlier) was not the operating system as today is intended but a bunch of Machine Language routines to handle the 1541 and 1571 floppy disk drives. CBM BASIC was what we could call today "an Interface" to send command to the drives (and datassette tape!) in an easy way, though you could use Kernal Jump Table to load, save and do whatever you want directly in Machine Language. CBM DOS is stored in a ROM directly on the 1541/1571 not inside the C64 OS. The Machine Language routines to handle it are into the C64 Kernal.
I could agree that MS-DOS was an OS and I perfectly recall the days when there were IBM-DOS, MS-DOS and so on which were not 100% compatible.
Though rest the fact that DOS is *not* an OS as we consider Windows/Linux/MAC OS today.