In the Diocese of Salt Lake City, the Bishop’s Residence is a fabulous home, with a HUGE parcel of land in one of the most tony neighborhoods in the city. That is what the press would print. The rest of the story: The residence was donated to the diocese a few years ago by a very wealthy convert. The Bishop spends 1 MAYBE 2 nights a week there. Otherwise, he has a modest apartment next to the cathedral. The residence is used mostly for gatherings; when the Bishop or diocese is hosting.
I saw a similar case with St. Joseph’s Church in Middletown Delaware. Th priest there is an honored guest to Catholics there, but his actual owned house is one block from the church, and just a little larger than a trailer park home.