Definitely a component. I cannot imagine anybody judging fairness without consideration of self-interest. Take the example of the game in the linked article.

If it's a one-off interaction and if there is no penalty for lack of charity, then I am keeping the $10 and leaving you as you arrived. Tough luck.

1. If there's a feedback system -- you get to reject my offer, then I am more likely to offer you something than to offer you nothing -- you'd reject my non-offer just out of spite (or lack of "fairness"). If it's a one-off interaction with feedback I may offer you some amount less than 50% in hopes that you will accept a smaller portion and me retaining the larger portion. but not so great a disparity that I raise your ire. Will you accept 30%? It's one-time offer. If it fails, we both lose the money. Is $3 out of $10 (or $3M out of $10M...) better than $0?

2. Let's make it even more realistic -- it is now a repeated game. There is an undetermined number of rounds in which I get $10 and can give you any portion of it and you can reject it without affecting the subsequent round.

I'll bet a dollar that you would eventually start punishing me (rejecting the offer) if I offered you less than 40% each round. Eventually it's going to approach 50%. But it will never get to 50% because I'm always going to have the advantage.

3. Now let's say we alternate the game each round. I'll bet we'd settle into a pattern that over the long haul would be almost exactly 50%.

What do you think?