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In any case, a news organization would not want to be dependent on a license from twitter if they did not have to. It costs them nothing to ask for a separate license from the person who took the video, and who therefore owns the copy. Notice that they aren't offering to pay anything.
If only 1 in 1000 people would later sue over such use, even if the suit was tossed out early because of the twitter license, that still costs the news organization something to defend the suits, and it may make them look bad. Asking for permission seems liker a very sensible practice for any such organization. If permission is refused, they might try to go ahed anyway relaying on the twitter license, or they might not.