I have been in a similar situation with a family member. Fortunately, we were all rational beings that understood he was essentially dead and would never be coming back.
We made the decision to take him off life support after 2 days.
So yes, I have walked in their shoes and they are being irrational and need someone to step in and say enough for the sake of that poor child.
Here's an ideal that I've been contemplating in light of comments like Jana's above. I'm NOT advocating it, just putting it out there for review and I realize my comments are addressing a hypothetical using Jahi's case as a catalyst, not as a direct example:
If we agree that brain-dead is dead, and that dead means all sentience has ceased in this temporal plane, then it would follow that we also believe that
a) the transcendent part of the person (if we believe there is one) has entered into whatever eternal state comes next and is beyond the reach of any intervention (not intended to open debate about those options here) and;
b) the body is beyond physical suffering as the mechanisms necessary to register any such conditions are completely absent.
Supposing this, what then is the difference between the present state of this body and one that's been donated to research? How is the indignity any greater than being chemically preserved, dissected, poked, prodded and observed for months or years on end in the interest of advancing medical science? Other than our visceral reaction to the concept is there truly a material difference?
Again, I realize the case at hand does not fit the scenario I've proposed, but all cadavers were once as Jahi was - living and loved, and now are no longer.