I am pretty sure that's exactly right.
The CCD takes in far more than it presents as the finished image, and all the hard work is then done by CPU and presents a slightly, smaller round the four edges, image.

The overlap of the original is needed to stabilise the image if that makes sense...........

I don't mobile phones uses a lens based OIS, it is the sensor that moves not the lens. Why they can not cope with different frame rates and resolutions I have no idea.
My Panasonic G80 has Image sensor shift and that works with all modes and frame rates, right up to 4K 30FPS.
So maybe it is something to do with the CPU processing power,