Can't explain the "fog" which was aparently seen,so we'll just have to take their word for it.
A flash was definitely not used, but this picture did not use a "fairly long exposure time", as that would require a tripod, otherwise the shot would be blurry. This picture is sharp so I would say that the exposure time was fairly short.
If it was a long exposure (I say it isn't), and someone moved out during the exposure time, then why is the face all that is seen? And why is the face fairly sharp?
I have also done shots like you describe here but this isn't one of them.........there are lots of tricks that could have been used to make this photo, but if we believe RockabyeBillie and her mother that this is not a trick or deceptive photo, then we just have an unexplained face or something that resembles one...