That’s a common misconception, but it is not strictly true. There are fair use exceptions even for profit. For example, if a news station wants to report on something, like a movie, they can show a short clip of it to accompany their commentary, even without permission of the person who owns the copyright. And news stations are certainly run for profit.
Courts are certainly more likely to rule that non-profit uses are fair use, but there are many commercial uses that still qualify as fair use as well.
No misconception on my end. 17 U.S.C. § 107 specifically provides that "criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright [emphasis added]"
Although I agree that "fair use" may apply in limited commercial settings, I dispute your statement that the use of the video "clearly" falls within fair use. It is anything but clear.