How would you handle this Dementia-induced obsession?

My client is a bit more strong physically than he was a few weeks ago, but his Vascular Dementia is progressing. He has been obsessed with something from day one (back in late summer) and some days it gets to be very detailed and scares him. The gist of the story is that, while he was in the hospital (sometimes he says this was a few weeks ago, sometimes a year, sometimes days), the "city" moved his house, and his neighbor's house, to their current location.

Sometimes the story gets very lengthy and complicated, and the house isn't his at all, but was moved there by the city and now they have to live there, but it was free. He doesn't know why it was free, and what scares him sometimes is that it could be taken away again as easily as it was given.

How I've handled it so far is to take him for a walk around the house and inspect the foundation. It looks great. I also take him for walks through the neighborhood to talk to neighbors on both of the days I'm there. He converses with them all. While he's lucid I engage him in conversation about the benefits of living in the same place for so long. He agrees and is "present". Then, all of a sudden, he will start in on that house moving thing again.

One day, when he was getting agitated, I took his arm and I said "Do you feel safe here?"
He said "Yes!"
I said," then, maybe that's what's important."
He instantly calmed down. Immediately I pointed out something else, and that conversation was dismissed.

Here's my real question. What if I got the plans from the City - showing his home being built where it is? I know not to argue with Dementia, I know how to join a person in the journey. But because this comes up every single day, and seems to be causing him distress, should I try to correct his thinking?

He accepts it when I tell him that the stroke he had stole some of the words he wants to say. He seems comforted by that. I tell him that, when he had the stroke, some parts of his brain were hurt, and those parts were where some words are reached. He understands this, and now he talks to me and lets the missing words just go missing. He lets me figure it out! Like yesterday - "We went to that place where we............ get everything." "Lowe's?" "YES!!!!!"

Yesterday I drove my truck and let him take me on a tour of the entire town where they live. He never missed a turn. Described everything.

So, I'm baffled. And obviously long-winded.