You can do it either way, but in the video I noticed that you animated the rotation. It seems intuitive since you only rotated it, but that rotation was based on the 3d cursor and not the origin of the camera, so under the hood you are both rotating and moving the camera’s origin at the same time. If you key location and rotation you should get the right effect!
Parenting it is another valid solution, so if that works in this scene then stick with it!
