It's a bit of an exaggeration (though not by much). In one episode, when Pinky thought no one wanted to be her friend any more, she became severely depressed, represented by her hair going flat and straight. (It was like that when she was a child, too, but she wasn't depressed then; it was just a dull childhood.) As her depression deepened, she started losing touch with reality (which is saying something for Pinky) and having dissociative episodes, such as hearing inanimate objects talking to her.
As with many character aspects, portions of fandom have blown this out of proportion for various reasons.