A lie? You’re “not so sure,” but you’re calling it a “lie” anyway? Your argument isn’t with me, it’s with Batnard College.
It’s Barnard who advises its students to list on their resumes “Barnard College, Columbia University” or “Barnard College of Columbia University”.
If an employer asks to see their diploma, a Barnard graduate can show them theirs with the Columbia seal on it and signed by the Columbia president as well as the Barnard president.
The front gates through which you enter the Barnard campus include “Barnard College of Columbia University” in large, permanent metal letters.
Barnard faculty are evaluated jointly for tenure bu both Columbia and Barnard.
It is so integrated into the university as a whole that when Barnard students choose a major, their options include those offered across the street at Columbia College as well as those offered on their own campus.
A lie? These battles were fought years ago and were resolved years ago.