I agree, and I have a theory/dream that this same principle can be extended and to all identities, including gender, sexual, and political (which are all subset of culture, of course). The value of having these discussions over a meal may be in part that there are certain expectations of social behavior in play, so people tend to be on better than normal behavior, and everyone knows they're going to be there for a while anyways so might as well make the best of it. As a result, it facilitates an environment where people actually listen to what other people are actually saying, rather than relying almost entirely on subconscious, preconceived notions, as is what routinely happens on internet forums. This extra time and dialogue helps bring people's perceptions of reality, in this case their understanding of the beliefs/culture of others, more closely inline with reality itself.
In a sense, discussions over a meal forces good behavior on people, and the result of that is that people realize their preconceptions were off the mark. Absent a meal and the social structure and expectations/rules that come with it, and particularly in the case of internet discussions where there is no physical presence and often no strongly enforced behavioral expectations at all, we're left to rely on rationality, conscious awareness and personal discipline, things that aren't really taught or practiced in certain cultures. I'm a big believer that this is one of the key enablers of the increasing polarization we are witnessing in our societies, Western societies in particular.
People come from different nations, a country that allows different nations to exist in the same physical space is a great way to bridge that gap and food seems like a good starting point. Anyone can probably gain some appreciation for some culture if the food is good( like, this culture actually has something worthwhile to show). I think it works in a subconscious level. Also given the lack of worldwide history education it's also an interesting way to get people in a first contact with a different culture.
The best way to build a bridge between peoples is through culture, and food is an important part of culture.
The next step in bridge building is sharing meals with people of other cultures. Starting or strengthening friendships around food is a great way to lessen the power of prejudices, and put aside our national identities for the benefit of sharing a common bond as humans through our cultural identities.
Edit: even though the stated reason in the article has a political motive, I still think it helps at a human level.