The way I see it, interdependence is just dependence with a nicer name. Independence should mean you can still stand on your own if the network breaks. Calling reliance strength feels like changing the word, not proving the point.
Honestly, my opponent's point about there being no god doesn't really touch the question about independence. That might be a fair point somewhere, but it isn't here. My gut still says leaning on everyone isn't the same as standing on your own.