The “Old Row” designation/perception has been around a very long time. The fraternities considered Old Row were originally those well-established chapters built along University Blvd from one end of campus to the other. The newer “New Row” fraternities were primarily built on a new “row” (Fraternity Lane).
The sororities considered Old Row were typically strong-recruiting chapters who participated in swaps and other social events/joint parties with the Old Row fraternities (including campus politics). With sororities, Old Row did not (then or now) refer to sorority location (unlike “First Circle,” which originally did refer to the location of DDD, AGD, and KD). “Old Row” also does not refer to the oldest sororities on campus.
Traditionally Old Row chapters (fraternities and sororities) were associated with a lot of in-state alum involvement, in-state connections, money, and legacies – thus the perception of prestige. The t-shirts are “new,” relatively speaking (is there any occasion or party that doesn’t warrant a t-shirt?), but as far as extra cost or the extent of Budweiser involvement, I haven’t seen much other than unsubstantiated internet gossip on those points.
The handful of sororities considered “Old Row” continue to be strong-recruiting chapters and in-state strongholds. However, in-state PNMs are the minority now, and IMO, the Old Row perception exists mainly in the minds of in-state PNMs (high school/hometown influences). All the chapters at Bama are robust and packed with sharp girls and opportunities (which will be clear when you see the ACRES of accomplished and lovely PNMs who will become new members of every chapter on campus). Just disregard talk regarding tiers prior to (and especially during) finding your chapter home.
That goes for rumors about Chi O probation too – Chi O is alive and well. You can check their member numbers and grades from last semester here (their pledge class had highest GPA on campus):
http://greekaffairs.ua.edu/documents/TheUniversityofAlabama-Fall2014GradeReport.pdf
Good luck to you. Hope you have a great recruitment!