The sub-channels buy the syndication/rerun rights. It is generally more lucrative for a company to sell the syndication rights than it is to run a network with all the headaches involved and buy their own rerun rights (yes, they would have to buy their own programs to reair), find advertisers, get distribution.
Nick at Nite/TV Land could buy any programs they like. They are owned by Viacomm/CBS and could buy whatever syndication rights they want. They choose to play back what they play back because according to their marketing department, they get more viewers and make more money. Just that simple.