I'll probably regret this, but I'll bite. Why in God's name would you ever do THAT?!?
Not a risk I'm up to taking, but people also do that (non-Indians-homes and businesses) on Indian reservations and putting up vacation homes/cabins, where allowed, on some public lands out here.
Oh, and in a town near me... there is a neighborhood of remodeled craftsman style houses on land that the city owns. Land has some historical designation and is owned by the city. Buildings meet some historical criteria and are privately owned. Yeah, nothing to go wrong there!