Although this is probably technically true, in actual practice, school use of copyrighted materials has historically been treated quite liberally. Teachers often copy whole chapters from books, and do other things that strain the definition of “fair use.”
However, after doing a little Googling, I find that there is something called the TEACH Act, an amendment to the Copyright Act, regarding use of copyright materials in the classroom.
The TEACH Act amendment to the Copyright Act, codified at § 110(2), permits the performance of a reasonable and limited portion of films in an online classroom. Under the TEACH Act, there is the express limitation on quantity, and an entire film will rarely constitute a reasonable and limited portion. Using the TEACH Act Checklist will help instructors to comply with the requirements when showing films in online classes.
Looking at the checklist, one finds that it is acceptable to show “Entire performances of nondramatic literary and musical works,” but only “Reasonable and limited parts of a dramatic literary, musical, or audiovisual work.”
Which corroborates your librarian’s statement WRT most Hollywood movies.