I just really do not think that DL would contact a group to reissue to a different flight the same day AND still sell tickets on the flight. The likelyhood of DL selling that many last minute Y class tickets that they then proactively moved a tour group instead of working it out at the airport is frankly absurd. A ton of people on that plane do not have JFK as their final destination. It would make way more sense to route some people through AMS and CDG to then to their final destination for individuals or small groups than move one big one.
If I may wildly speculate for a moment...the tour operator couldn't get transportation to the airport in time for the first flight. Either they forgot, or it fell through or whatever. Then they had to change the flights at the last minute. And if you're the tour operator at this point you just put all the blame on Delta.
What is more likely...DL overbooked (for whatever reason) a flight so much that they proactively reached out to a tour group to move their flights 24hrs in advance OR the tour operator screwed up?