I still want to know what the official reason for outlawing "Tri Sig" is, if there is one . . . I think the thread makes it more complicated, rather than clearing it up.
The whole "We're not Tri Sigs, we're Sigma Sigma Sigma" thing doesn't really make sense to me, considering the fact that then you would also rule out any other nicknames, including the supposedly acceptable "Tri Sigma" and "Sigmas."
Of course it's the sorority's decision to call themselves whatever they want, but without some sort of significant justification I think they'll always be fighting it -- there are people who are always going to refer to it as "Tri Sig."