Pixel binning is a form of resizing, so yes If I took an 18 or 22mp still and resized it to 2 mp, I am pretty sure it would look better and crispier than if I paused a 1080p feed. Maybe I did not explain myself better before.
There are a couple of reasons why a single frame from 1080p won't look as good as a 2mp still, and I'm pretty sure a lack of resolution doesn't come into it.
First of all, the video will be compressed very differently from a jpeg - its not just lossy compression of areas of the image, but between frames too. Secondly, when set optimally, the shutter speeds will be very different between the two. Typically with moving subjects, in a photo you'll want them free of motion blur - in a video, to avoid that stuttering effect, a slow shutter speed is needed (because of the slow frame rate) to allow motion to flow from one frame to the next.
The two really can't be compared, but if video ever gets to the point that NHK were on about - 120fps, higher shutter speeds on each individual frame will be optimal, further narrowing the difference between video and stills. However, current broadcast TV is 25 or 30 fps, so no optimally recorded 1080p broadcast TV will be able to freeze frame to create a still image as good as an optimally taken 2mp photo.