You are completely correct I think. I believe they want a copy of your current transcript as well as one from any institution that you received a prior degree from?
I quote from the e-mail I received:
"Pleasearrange to have official transcripts from your currentacademic institution (if enrolled) and allinstitutions from which you received a Bachelor’s or Master’s or doctoraldegree sent to: OFFICIAL TRANSCRIPTSU.S. StudentProgramsInstitute of International Education809 United Nations PlazaNew York,NY 10017 IIE mustreceive these transcripts by March 1, 2011 at the latest in order for you tocontinue to be considered for a 2011-12 Fulbright grant." .