You can't have it both ways.
All I know is this: there is no such thing as a national, constitutional, official bond between any NPC group and NIC group. I don't know why anyone in a sorority (other than Zeta Phi Beta) would want to muddy the waters by referring to anyone as their "brothers."
Delta Gamma brings up the Phi Delta Theta connection on their website, but they also say that it's a myth that they are their "brother" fraternity. I see several individual AXiD chapter sites that refer to the Sigma Nus as brothers, but on the national website, while the support and contributions of Sigma Nu are acknowledged, the word "brother" is never mentioned.
http://www.alphaxidelta.org/heritage_founders.asp
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