I just tried testing with a DIFF without a FULL in a similar way I tested with INC. I ran a DIFF manually with no FULL and it threw out an error. But if I let it run via a SCHEULED backup it started properly, though as FULL instead of a DIFF.
EDIT:
And as with my test with INC, this is working as I would expect it to.
EDIT:
And as with my test with INC, this is working as I would expect it to.