I didn't see the programme myself, but I have seen examples of this before. People that have an estate that has been in the family for centuries, but - to put it bluntly - don't have a pot to piss in, and have to turn to National Trust for help, even if it is just for a handful of tourists to walk around their home.
You do wonder what Mr and Mrs. "Fortherington-Farquar-Smythe" can possibly need a 20-bedroom Country house for, but of course, I suppose many of us in the same situation would be just as determined to not let it slip into the hands of someone else, with so much family history.
I just wonder why more people don't turn it around by converting it into a hotel. I wonder how much of it is down to pride, or more than likely, again the likes of the National Trust cannot allow it !