Yes, I would IDB Virgin. Strangely enough we occasionally see the BA version of this: when AA swipes inventory to put their irrops on to BA, when in fact the flight is oversold.

It's a quirk to how the revenue management systems work close to departure. We all know about how flights are overbooked due to no shows and indeed irrops, and in the middle distance that all works fine. But at the gate, and when standbys and staff standbys are in contention, then J9, C9, D0 may be an oversold flight - economy ticket holders have to be upgraded into business to make it all fit. Really it should say J2, C0 - they can take maybe a few passengers. But when you have to rebook an entire aircraft, the computers merrily accept the bookings, and may even refresh J9 back to J9 after selling 9 seats. The system works until you try to do something strange like replace 15 trans Atlantic services all in one hour. It drives gate staff up the wall.

But that's not the passenger's problem (ok, it may become their problem) and in your case, and unusually, you had a boarding pass. To my mind that is copperbottomed IDB, keep the boarding pass. And your claim is to VS not BA on that one. VS can blame BA as much as they like, and can send them the EC261 bill if they want. I actually think it's VS' job to do your Right to Care too, but probably BA would be less hassle.