I used the YouTube API to play a series of videos hosted by one particular YouTube channel of national (US) prestige. About a month later, I received a letter from one of their attorneys requesting to remove the "republished" videos since permission was not granted. They pointed to the YouTube terms of service (5B):
You shall not copy, reproduce, distribute, transmit, broadcast, display, sell, license, or otherwise exploit any Content for any other purposes without the prior written consent of YouTube or the respective licensors of the Content.
However, my research and re-reading of the terms seems like it's pretty cut and dry that if the embedding functionality is offered, it's fair to use (non-monetary purposes at that) (6C):
You also hereby grant each user of the Service a non-exclusive license to access your Content through the Service, and to use, reproduce, distribute, display and perform such Content as permitted through the functionality of the Service and under these Terms of Service.
These two sections seem in conflict with each other (You've granted permissions for users to do these things, but "under these Terms of Service" they must receive your permission?).
What I've read (Quora, blog posts, etc) suggests that what I had built violated no copyright and was well within the terms of service.
I've taken the material down, so I'm not looking for specific legal advice in this specific situation, but I am curious about how this community would interpret this situation. Right or wrong, I have no time, money, or energy to fight them for what was a single page side project, but given how pervasive embedding YouTube videos is, some clarity on the above two clauses would be valuable!