I have 3 daughters (and 1 son.) One daughter and my son have always wanted to be very self sufficient, but my other 2 girls crave a LOT of attention. Kids discover early that adults will respond quickly and completely to fear, but not other situations like boredom. So, when my girls wanted attention and didn't feel they'd get the desired response from us or other adults by just engaging in normal conversation or asking us to play, they would put on a big show of being terrified, or in agony, or unable to so something for themselves (even something simple, like opening a door.) I had people stare at me like I was a monster when I would tell an apparently overwhelmed, wailing child to "stop that now," but then they'd be amazed that it would stop like a switch had been flipped. (My kids are very good little actors. ;P) I've just had to explain to them over and over (and OVER) that it is indeed possible to get someone's attention without a huge crisis. They're better about it around their dad and me, but still likely to be very overdramatic to other adults. It's the lure of immediate, complete attention.
I'd suggest that you keep responses to her fears very short and matter of fact, and give her much more exaggerated attention in normal settings - when she's coloring, playing quietly or whatever. The idea is to get her to see that she can have, and even ask for, attention in ordinary situations.