On the Internet Movie Database, we find the following regarding Singin' in the Rain
The American Film Institute voted the movie #10 of all time, the highest rated musical of the list.
Now, we might conclude from this, after viewing the American Film Institute's list, that neither the author of the bit of trivia, nor the editors of the IMDB, have seen the list in question, because their information is patently false. The highest ranking musical (and, IMO, the greatest movie ever made, but that's another issue) comes in at number 6: The Wizard of Oz.
Such a conclusion would seem unfounded, however, as they did get Singin' in the Rain's position right (number 10).
So we might conclude, instead, that they had not seen the Wizard of Oz, and thus didn't know it was a Musical. This suggestion, however, borders on lunacy based on the other available evidence. That the editors of the largest movie database on the web would not have seen the most watched movie of all time (having been seen by over 1 billion different people since its debut) is unfathomable.
Perhaps, then, they had seen it, but still wouldn't classify it as a Musical? Firstly, if we're not going to call a movie produced by Arthur Freed, with much song and dance, and songs that develop the plot, a Musical, I'm not sure what we should call it. Strictly defined, it meets the criteria of a Musical better even than the quintessential Musical Singin' in the Rain, where the songs are largely incidental, and used to give Gene Kelly and Donald O'Connor a chance to dance.
Secondly, that they know it is a Musical is undeniable: They tell us as much on their page on MGM's masterpiece.
The most reasonable conclusion is that, as it often is, the Wizard of Oz was excluded from their frame of reference by virtue of being a children's movie. It simply didn't occur to them to include The Wizard of Oz as a Musical. Their silence on the Wizard of Oz betrays only their own lack of thorough consideration, not their lack of knowledge.