Well, I wouldn't presume to tell any SAIs the status of their own group.
I can tell you, though, that our
Centennial History says this about our own efforts to avoid being co-ed in light of Title IX (which forbids colleges that receive federal funds from housing single-sex orgs, but which includes an exemption for "social" fraternities and sororities):
Two of the three major fraternities for women, Mu Phi Epsilon and Delta Omicron, responded to [Federal Department of Health, Education and Welfare] pressure by becoming coed nationally. Sigma Alpha Iota did not; instead, they filed an appeal with HEW, claiming that Sigma Alpha Iota existed:
"... to foster interest in music and to promote social contact among persons sharing a general interest in that art form rather than to prepare persons for professional endeavors relating to music."
On the basis of this statement, HEW granted Sigma Alpha Iota an exemption from the requirements of Title IX.
Phi Mu Alpha Sinfonia: A Centennial History, T. Jervis Underwood, p. 6.17 (2000). Our histories always give the impression that we got our idea for seeking an HEW exemption from you guys.
Of course, histories otherwise may be different -- we have generally seen our claiming "social" rather than "professional" status as a return to our roots and the values on which we were founded, having been founded as a social rather than a professional fraternity. Needless to say, I don't know SAI's history like I know Sinfonia's.