Yes, and no. Yes, and no.
Kasha,
What does that mean?
The choices are mutually exclusive. Either Iyov existed, or he didn’t. Either Beis Din executed a Ben Sorer UMoreh or they didn’t.
In any event, this proves that your statement about Chazal not arguing metzius is clearly wrong — as both of these arguments exist in the Gemara.
The Wolf