It's easy to imagine what could have happened. The cabin crew wouldn't make the announcement, so they started telling the people sitting near them and asked them to pass word along the plane. They claim all the passengers were fine with this, but maybe someone complained to the cabin crew about it, or someone in the cabin crew got annoyed at the family taking matters into their own hands. Can quite imagine the crew/pilot getting shirty with the family and it's not hard to believe their response also led to the family responding angrily (although their asking others on the flight to come forward and support their version of events would suggest maybe most of the aggro came from the crew).
Unfortunate situation all around, although I would ask the family why they didn't inform the airline in advance? It's obviously an important issue for them and doesn't seem like something a parent would forget to do, especially if this airline doesn't have as clear guidelines as the others mentioned in the article.