What do you mean that's all she can do? How about going to the American embassy in Panama and going through the process legally? Seriously, you think it makes more sense to travel to Mexico, enter illegally and hope all the legal issues sort of work out magically?
Going through the embassy means nothing until she actually can prove her sire. And she had no money to buy advocacy with. So, she had to do it the hard way.
My BIL's niece (hence my niece) is going through the same sort of thing. Her daddy made sure she was dual citizen (down in Costa Rica) so she could claim her rightful American heritage through him before he died... It has been a terrible and winding four-year slog for her regardless... One she could not even attempt without my BIL's sponsorship.
She is here, and when her citizenship is finally through, she will bring up her son (who she hasn't seen in those four long years), who is also by right, an American.
You make it sound like a piece of cake, but even if you have a legitimate claim, it is a hard row to hoe. For someone without income, the cost prohibits any movement forward.