The name of the camp — "Niggerhead" — was first reported by the Washington Post on Saturday. The paper said the name was painted on a rock at the entrance of the property.
Perry reportedly began hosting fellow lawmakers, friends and supporters at the secluded ranch early in his career. The offensive phrase has been painted over, but the Post's sources and the Perry campaign differ on when that was done.
The Post reports that the name can still be seen through the paint.
"My reaction is, that's just very insensitive," Cain told Fox. "[There] isn't a more vile, negative word than the N-word, and for him to leave it there as long as he did, before I hear that they finally painted over it, is just plain insensitive to a lot of black people in this country."
Longtime hunters, cowboys and ranchers said the place was known by the name as long as they could remember, the Post reported. The name on the rock was given to mountains, creeks and rock outcroppings across the country in earlier times, the Post report said.
Ray Sullivan, Perry's communication's director, pushed back against the Post report on Sunday.
Sullivan said the governor's father, Ray, painted over the name in the early 1980s. That conflicts with the accounts of seven sources who spoke to the Post on the condition of anonymity. They claim the offensive name was visible during the 1980s and 1990s, when Perry launched his political career, with one source saying the word could be seen as late as 2008.
Sullivan, in a response to NBC News' Carrie Dann, disputed the accuracy of those accounts.
"The rock was obscured in 1983 or 1984 and remained so," he said. "Named interviewees in the story corroborate that. The story has no named sources seeing the name on the rock in later 80s and 90s claim and those unnamed sources contradict one another."
Sullivan said Perry's last visit to the property was in December 2006, and that he stopped leasing it in 2007. The Perry campaign says the story's suggestion that Perry brought guests to the property when the offensive language was visible is also false.
When asked about the name on the rock last week, Perry reportedly told the Post it is "offensive name that has no place in the modern world."
The Post reported that the phrase was still "faintly visible" beneath a coat of white paint as recently as this past summer.