DTSMUMBO, the NHS treated the daughter for a month before she reached the point where she was ready for discharge. On any interpretation, she has to have had a serious condition. How does that equate to a scam? Do you seriously believe that, with a serious illness, they risked their home and travelled to Barnet just on the off-chance they would get a holiday there? Does it occur to you that, for instance, they may have been sent there by their local hospital?
The fact that the daughter is now doing a college course in Barnet is a matter of considerable credit to her, given her difficulties, and probably reflects the fact that they have no home in Grimsby and no realistic prospect of getting one. It doesn't necessarily mean that they have no long term intention to leave the area - it may be a one year course, or it may be one that is transferable to another college.
Where does the report say the hospital has refused to involve Barnet? I suspect the hospital don't care where they go so long as they can satisfy themselves that it is appropriate accommodation.