Normally there isn't a V fare, just V inventory, so unrestricted or not has nothing to do with it. Similarly, if you upgrade into business class using a SWU or miles, full Y or B or M all upgrade into V class, as would H Q K fares for a "domestic" segment marketed as business.

Does your corporate travel site really show you a V fare, for instance with a fare code looking something like V0A14XYUP, or does it just give tickets booked into the V inventory class with a different fare code not starting with the letter V?