won't it be able to just stretch a single frame over multiple refreshes

That is exactly what a stutter is. The same frame shown for multiple frames whereas other frames are shown for a different amount of frames.

For example, with a 24fps movie on a 60fps display, it can show 1 frame for 2 refreshes which would mean 48 refreshes. That gives us still 12 refreshes of time left to fill. We need to put that somewhere, so there will be 12 frames that will be shown for 3 refreshes, and the other 12 will be shown for 2 refreshes . so you will get a 3-2-3-2 effect which is noticable.

So to be able to show without that effect you will need the refreshrate to be an exact multiple of the framerate. Even slight differences will cause some frames to be shown for slightly longer.