I emailed them with the same question. Here’s what they said:
…
Hello XXXXX,
Thank you for your email and congratulations! For helpful information on scholarships, please visit http://www2.binghamton.edu/financial-aid/types-of-aid/scholarships/binghamton-scholarships.html . Merit aid is a possibility. All the best.
Sincerely,
Undergraduate Admissions
Binghamton University, State University of New York
…
So when they say it’s a possibility, I think they’re implying that it’s pretty rare. 