Sawako
Could you attach the link regarding to the news about it?
I can't say anything about it due to unclear information you gave. It's not clear the background of the parents, perhaps they're not native Japanese or had been overseas for a long time, or maybe they're just being a "modern (extreme maybe)" parents.
People is like a pendulum, an individual could be against what some society believe.
I'm an Indonesian, I personally will say "Mari makan" which means asking everybody who are with me around the table to eat or at least excuse me for having my meal. It's not a must but it's nice as a courtesy to others.