I think that all the responses here are correct but none of them apply to the OP. My understanding is that the "V" fare bucket is just the upgrade bucket. Medallions do see "V" (or, sometimes, other fare classes) as the fare when their coach tickets get upgraded but the "V" bucket isn't reserved for medallions.

Our corporate booking engine also sometimes shows the "V" bucket, which in my experience works exactly like Q-up or Y-up fares. Basically, you book a coach class ticket but get an immediate confirmed upgrade to first class, which has nothing to do with being an elite.

Just like Q-up and Y-up fares, however, you have to remember that this is still technically a coach class ticket, so that in the event of flight changes/irrops, you'll only be eligible for a coach seat on another flight.