That's not a good enough reason for the TV show though.
It's strange to me that they didn't think up a proper reason for Claire to seek out Luke. It's just, like, Oh I've decided all I want to do with my life now is help random super-heroes - hey! Look who's on TV! I know that guy! - and I'd rather do it in Harlem than Hell's Kitchen because, uh, well, this is where this series is set. Nope, I don't seem to have anything to do but help and motivate Luke Cage, but I do have a very useful random net of contacts who will steal ambulances for me and stuff.
It's weird that they didn't give her a plot to give her some more motivation to be in Harlem, and to seek out Luke. Wouldn't have been hard, just tie her family into some of the shit Cottonmouth is doing.