Even if the person takes financial responsibility for the dog, he is keeping other needy animals from getting into rescue because he is listed as the rescue contact for the area. Some people just like to tell others they do rescue because they like the sound of the words and idea. Power-mongers There are people who do rescue by themselves, do a good job, and are a real asset to their communities. There are also people who draw all the attention they can to themselves, not for money, but for the ability to control. This is not always bad.
Rescue needs the outgoing person who draws a lot of publicity.
But if you do this for any reason other than to help the animals, you are doing more harm than good. If you use your position to control finances, placement of animals, publicity, or anything else without making the animal the top priority, you are not needed in rescue. There are people doing rescue who get something crucial from the animals that they aren't getting from their own animals or from the people in their lives. I have always said that we get more from rescue dogs than we give. They teach so much about dog behavior, breed specifics, resilience, stamina, the ability to love and keep loving, and the ability to heal and love again.