^^^ I know quite about Masonic history and the history of GLOs in general and particular. Thanks all the same.
An understanding of connotation and common usage are key. While Masons and masonic writing frequently refer to Freemasonry as "the Fraternity," the general public doesn't. Indeed, you say "it might be slightly misleading to people who don't know about or understand Masonry." That would be the majority of Americans. Ask the average American what a "fraternity" is, and you're going to get a description of a college GLO. Anything beyond that would be viewed as a fraternity "in the broad sense" of the word, not the narrower but commonly assumed sense. That's why I said:
"when a statement is made along the lines of 'all but 2 US presidents since 1825 were in a fraternity,' the almost universal understanding is going to be a collegiate, general (social) fraternity. This is especially true since this statistic is usually cited in rush materials or responses to criticisms of the Greek system."
If the claim that "all but 2 US presidents since 1825 were in a fraternity," was meant to include Masons, then anybody wanting to be understood would say "all but 2 US presidents since 1825 were in fraternities and/or were Masons." Otherwise, it's a trick question.