I used to work there. They try to make it difficult, but they know they can't because it's funded by taxpayer's money.
Just have a good reason for wanting to watch the video. (Just because you missed it on Broadway isn't a good reason). You need to use it as a source for collecting information for a paper, or news article, or production.
My suggestion though is to call them ahead of time if you have a specific show in mind. Some of the videos need permission from the author.
If anyone ever tells you that you put too much Parmesan cheese on your pasta, stop talking to them. You don't need that kind of negativity in your life.