From what I can gather, the White House didn't explicitly ask for the clip to be removed. Rather, they suggested the clip might violate YouTube's own terms of service.

From the article:

> White House officials had asked Google earlier on Friday to reconsider whether the video had violated YouTube's terms of service

Still, the net effect is the same. The gesture was made with the goal of having the video removed from YouTube. It's unfortunate that our administration went down this path at all.