This is wrong, you'd still have a operating system: BIOS
BIOSes offer system calls that tend to be backward compatible, so it's an OS of sorts.
(I don't disagree with you -- UEFI provides BootServices which arguably are more numerous than the number of syscalls on most operating systems. Just that "system" being in the name isn't really the best argument. :P)
It's quite the same as DOS being 'disk operating system' - it was able to drive the floppy and provide a file system.