There is no 1st Amendment right to have your content hosted on YouTube. YouTube is a private, commercial venture that can remove your content for any reasons at any time. In fact, to say that YouTube must show all content and not remove any content and otherwise people's 1st Amendment rights are "interfered with" - would ironically take away the very basic right of YouTube to do as it deems fit in its own domain, YouTube itself.
YouTube is free to remove content, and others are free to ask YouTube to do so. To say otherwise is to limit their freedom.
You tube has 1st amendment to do what they want is the point, they are interferering via pr and public peer pressure. Why is it not like hosni mubarik asking twitter to please STFU during arab spring?
If I remember correctly, Mubarak shut down the entire internet in Egypt during the uprising there. That's different than politely asking a single privately-owned website to please remove some stuff.
"YouTube is free to remove content, and others are free to ask YouTube to do so. To say otherwise is to limit their freedom."
YouTube is free to listen to anyone, but the executive branch of the government should not be the one asking. If it is illegal or top secret content, then fine and dandy, there are rules for that. Otherwise, it is an attempt to intimidate YouTube and squelch their 1st amendment rights.
I'm not sure how this was intimidation? It was a request, and YouTube declined it. That proves that YouTube's is free to act as it chooses. (YouTube could also have decided to remove it, regardless of the request to remove it, and that would be within YouTube's rights as well - and not contrary to the video poster's rights.)
YouTube is free to remove content, and others are free to ask YouTube to do so. To say otherwise is to limit their freedom.