BASIC is not the OS (try booting a C64 with just the BASIC ROM) just a usefull application,
It's the closest thing the C64 had to a native operating system, mate.
C64 BASIC is not supplied by Microsoft ( C= hacked the PET one as they forced them to sell it as is with unconditional rights on any future machines)
Right, that's why it said "Microsoft BASIC": because C= was in the business of selling pirated software. Regardless, was it written by MS? Yes. So I'm right - thanks for acknowledging that.
it ran on a 6510 CPU made by MOS

...a hacked 6502 - what I said still stands.