Hi OP, a friend of mine pointed this discussion out to me so I thought I'd dive in and respond.
My girlfriend and I were the contestants on the show you mentioned and believe it or not we have actually brought the question and its answers to the attention of the production company, although for a slightly different reason. We had a great time on the show and naturally felt gutted to have gone home with nothing but had happily accepted it until we discovered a problem with the question and the answers given.
I can understand the point you are trying to make that when the passenger figures for all of New York's airports are combined it would be one of the 'cities with the busiest airports' but I think basically what the question was asking us to do is 'think of the 10 individual airports with the highest passenger numbers and then name the city that they are in' (although this is not made 100% clear)
There are also different top 10's that they could have considered as you said: passenger traffic, cargo traffic and traffic movements.
Our dispute is with the figures used for the top 10. On the show, the top 10 tied in with the Airports Council International figures for the 'world's busiest airports by passenger traffic' for the year 2010. However, the most recent final figures were published in August 2012 and cover the 2011 period. In that top 10, Denver is demoted and Hong Kong moves up into 10th place. Carlyn said Hong Kong fairly early on and would have given five correct answers (based upon the most recently available figures) by the £41k mark, as you said.
We've been in touch with Victory TV and they are having their question verifiers look into it over the weekend, so who knows how they will respond. Anyways, I hope this gives you some insight into what's going on. I think at the end of the day, the researchers have slipped up somewhat and it has cost us a significant amount of money. Hopefully by bringing this to their attention it will help them avoid using an ambiguous question like this in future shows :)