From what i understand, slowing the shutter speed allows more light in, and usual, better pictures. This is if of course assuming the subjects are still. You're right though, slow shutter speed can result in better quality assuming what you're capturing is perfectly still.
speeding up the shutter speed captures a faster image, but being that it closes faster, less light gets in and the detail quality suffers.
Again, that's from what understood, but I'm no expert.
Edit: just to add though, I don't think this has anything to do with shutter speed and more to do with the ability to process images after the fact, along with lens size. Being that smartphones don't have the real-estate to have giant lenses, they have to rely on their ability to process an image after its taken, and in this regard, Google is king. From what I read, the camera actually takes photos slightly before and after you press the shutter button, giving them more than a few pictures to splice together to get the best result.
