Less like a real organization, and more like a loose alliance of people with similar goals, the Time Lords claim to be the only ones who can be trusted to police the cosmoverse. The Time Lords are people who have been erased from their home time stream, and now have no "home" world, no one who knows them, no place to go back to. Most Time Lords stumble into it through chance, they travel back in time and make some change in the stream that "erases" them. Some few peculiar individuals do this on purpose precisely to become Time Lords. But, either way, the Time Lords claim that because they have no home time line to defend, they are the only travelers who can be truly detached and objective. I'm simply not sure this is true.