Everyone is conflating whether this is an IDB with whether it's provable. I think it clearly is—a VDB doesn't mean that you agree to be bumped in exchange for any compensation and any flight, it means you agree to it for specific conditions. In this case I strongly suspect that's how the DOT would see it.
Proving that the passenger was offered a specific flight is more tricky, but a) there's always a chance one of the agents involved would tell the truth if asked and b) at the very least, you have the PNR history showing that the agents didn't confirm a flight into the record before offering the VDB.