Not exactly how it happened, I don't believe. They were always Nashville's team, but they had to play a season in Memphis while LP Field was finished, because Vanderbilt wouldn't serve alcohol if they played in the Dores' stadium or something along those lines. They were never going to be a Memphis team.
I think part of it is because they were supposed to play 2 seasons in Memphis, but there was no support, and Memphis smelled so bad or something like that, they played their 2nd season somewhere in Nashville. Either Bridgestone Arena or Vanderbilt's stadium, cannot recall.
Memory is fuzzy, but point is they were never going to take up permanent residency in Memphis.