I don't think that's right. For example, in the California Penal Code,
"A person is guilty of arson when he or she willfully and maliciously sets fire to or burns or causes to be burned or who aids, counsels, or procures the burning of, any structure, forest land, or property." [1]
The incendiary's ownership or not of the property doesn't matter.
[1] https://leginfo.legislature.ca.gov/faces/codes_displaySectio....