Quark's cousin Gaila owned his own moon and nobody seemed to think that was odd or unusual. Planets may be a dime a dozen in the future. Old Spcok appears to have spent no more than a week finding a new planet for the surviving Vulcans in ST09.
It doesn't matter as it's stated as fact that the planet was sold to Mr. Brack. No matter how it looks Kirk still had no right to take so much as a pebble off the planet. It can be assumed that there was no case to be made under "eminent domain" since they didn't bring that up after discovering that the planet was privately owned.