The light pollution fades the starlight coming from the Sky and this dont let people to see the Milky Way disc. Is there any study about this?
The biggest factor defining the minimum distance is light pollution from the particular city you are talking about. You can find light pollution maps here and here. You can also find charts here that describe the quality of viewing based on a combination of cloud cover, haze, turbulence and wind, temperature, light pollution, and other factors. They look like this:
The premise is certainly true. An exact distance isn't possible to determine since it would depend on how much light pollution is coming from the city, and how much haze (water droplets and particulates) is in the air. You could also be a "short" distance away but on a mountain with much greater elevation than the city.