I think because with this sentence the girls feels cold. like if I touch her, her skin is cold. And with "the girl isn't cold" they mean that she thinks the temperature isn't cold.
I hope this makes sense
"To be cold" and "to feel cold" are pretty equivalent in meaning. If you want to say that someone's skin feels cold, you usually say they "are/feel cold to the touch" to make it clear.
Tener frío generally refers to a person feeling cold, chilly. Estar frío is cold to the touch. From what I've read on the difference, the latter would be applicable if your skin were cold to the touch, whereas tener frío would be the sensation of feeling cold.