I believe that is the case, yes. According to information found on several websites relating to Italian dual citizenship, the grandmother can pass down citizenship to her children. However, the qualifications listed on the various official Italian Consulate websites vary(Chicago, NY, San Fran, Miami, etc. and are not so clear. For example, they might say "maternal grandfather" and not mention grandmother. Or, "maternal grandparents." But check out the info on this forum: http://italiancitizenship.freeforums.or ... y-t74.html
One other thing to consider, did her GGF naturalized after 7/1/1912? If he naturalized prior to that date then her GM even though she was born in the US would have lost Italian citizenship. After that date she is okay.