Without reviewing your video, which is something only your own IP lawyer can and will do, it doesn't sound like your description like there's any content in your video that you need permission to use. It's likely that YouTube wants to t agree to "indemnify" them, that is, pay their legal fees, if you're wrong and they get sued for something you did or didn't do.
To be really sure, you need to see your own lawyer.
Avvo doesn't pay us for these responses, and I'm not your lawyer just because I answer this question or respond to any follow-up comments. If you want to hire me, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. I'm only licensed in CA and you shouldn't rely on this answer, since each state has different laws, each situation is fact specific, and it's impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
Brad, if your entire video is only you talking to a camera, and you are not a minor, and you didn't have any other person help you shoot the video (or you have a signed contract from them if you did), and there is no music, no background, nothing else, then the legal answer is . . . probably.
As you can see, even in seemingly simple situations, there could be many issues to consider. Otherwise, you wouldn't need an attorney. Bottom line though, you cannot get advice from a website that you can legally rely on. It doesn't work that way. You need to hire an attorney for that. Then they can actually review your video and the terms & conditions of YouTube's contract or submission release, and give you an informed legal opinion. Without knowing these specifics, the risk of giving you inaccurate or incomplete advice would be too high, and no attorney is willing to risk that (especially for free) since it could be harmful to you & to them in the long run.
Best of luck!!
Please note that this answer should not be considered "legal advice" and no attorney-client relationship is formed by answering this question. You should hire an attorney licensed in your state and familiar with the relevant areas of the law to conduct an analysis of your situation and provide you with fully informed legal advice. This answer is posted for general purposes only.
Well, are you wearing anything with a logo or design or athlete on it? Are there posters or pictures in the background? Are you a minor?
There are a lot of little things that could require permission, or YouTube could just be looking, as one of the other attorneys mentioned, for an indemnification agreement. Either way, you need a lawyer to review your video, their correspondence, and any agreements or contracts that might be involved. That's the only way you're going to be able to really resolve the issue without maybe opening yourself up to legal exposure.
No information you obtain from this answer is legal advice, nor is it intended to be. You should consult an attorney for individualized advice regarding your situation. No attorney-client relationship is formed by my responding to your question.