I'm late to a thread again, but my two cents...
Quoting from Nakayama's book, Dynamic Karate, as the hips turn with the roundhouse, the supporting foot will pivot. Kept the foot solidly in contact with the ground and
make the pivot as small as possible. That's his language, not mine.
Another video from Kagawa Sensei, demonstrating a mawashi geri drill. Watch the supporting foot. You'll see no pivot, small pivot and larger pivot.
http://www.youtube.com/watch?v=Y08a0PAW5Rw&feature=related
For that matter, in the video posted earlier, watch to the end and note the supporting foot does not pivot at all in some of the kicks.
If you google some of the shotokan sparring (for instance, all-Japan matches), you will see some of the contestants do very rapid, relatively small roundhouse kicks with little pivot of the supporting foot, less than 45 degrees in some cases, so the body does not turn. For instance, Yahara's kick at 33 seconds here
http://www.youtube.com/watch?v=ufh6B-r_HOM&feature=related
Others, of course, do the classic and have a 90 degree pivot or more.
A roundhouse kick with little or no pivot of the supporting foot is a correct technique for some situations and some teachers. Kicking a bag with a large pivot may teach power and technique, but in a real situation, one may decide not to pivot and turn your body in the face of real resistance.
Although not part of the official JKA syllabus, there is something often called a "tournament kick", which looks just like a front snap kick until the hip turns and the foot curves out and describes an arc, striking like a roundhouse. There is no pivot of the supporting foot.
When I spar and the opponent is skilled, sometimes my roundhouse kicks tend to look just like what your instructor is showing you. Maybe when you demonstrate some skill in doing the kick this way, she will move you on to a more advanced kick including a pivot.
I guess what I am saying is that there is room for the kick as described in karate. It does not mean your instructor is deficient or incapable.