Personally I think this guy is wrong. I don't know him, but he sounds a bit pompous.
Common sense suggests that a CSA should not suggest that an adult travelling with two 14 year old girls should leave the girls behind on a Caribbean island. Even more so when apparently other options were available (e.g. asking for volunteers), because eventually the girls got on the flight.
I guess the most likely scenario is that he was travelling in Biz and the girls in Eco and Eco was oversold. Nevertheless, do not blame the guy, this clearly is a customer service issue. You simply do not make idiotic suggestions to solve a problem which in the first place is caused by the airline, not the customer.
As to Ladbrokes, Mr Bell has a responsibility towards their shareholders. It strikes me as an abuse of his influence to use his employers travel budget as a weapon in what is essentially a personal disagreement with BA.
With that logic, responsible CEOs should all be travelling Ryanair, but only if 1p all incl. tickets are available.
Probably the shareholders will be better off now that Ladbrokes will be shopping around for the best deals on whatever airline is available rather than automatically booking on BA because of some kind of corporate agreement.