When Hungry Kids Don't Eat

Hungry kids eat.  This is the premise of most articles on picky eating.  It's the premise that any good pediatrician works with when they discuss picky eating, and it's the one that nutritionists start with when they begin working with a new patient on how to create better eating habits in their children.
While this is an excellent premise, it isn't always true.  Oh, normal kids will eat if they get hungry enough.  But there are a few stubborn children who don't.
My oldest was the former.  She seemed picky at times.  There was the ball phase...where she would only eat food that was ball shaped.  Since this included grapes, peas and a full blown temper tantrum in the produce department over a bag of brussel sprouts (which she won; they were brussel sprouts after all) her pediatrician was more amused than concerned.  But the phases passed, and over the course of a month at any given time, her diet was relatively balanced.
Enter the youngest member of the family.  From the start, she had a cagey relationship with food.  She'd hungrily latch on and midway through a meal, arch her back and start screaming.  It took a few months and a bit of a rash to discover that she was allergic to the almonds and nut products in my diet.  As a toddler, she seemed to eat a varied diet.  Of course, it was limited in that we avoided anything with nuts.  But she ate squash, tofu, apples and cheese with relish.  She even tasted the lemon in a box of sushi we once purchased.  Somewhere along the way, she started getting pickier though.  Food couldn't touch any other food on the plate.  If a cookie or breadstick broke in two, she'd collapse into inconsolible tears.  'She's tired', we told ourselves.  Even if she'd slept well.
Then there came a variety of diagnosis for the rest of us.  Our family diet became more limited, and it seemed logical that she would balk.  We've been juggling this attitude for years now.  I don't want to be a short order cook.  But she needs calories.
Some nutritionists suggest using pediatric 'milk shakes' similar to ensure.  Unfortunately, I've taught the child to read and some logic skills.  She won't touch a chocolate shake for breakfast, and the ingredient list just makes her think I'm trying to hurt her.  They suggest occasional trips out, fast food is affordable and it's high in calories.  But it's never been in our diet so she gives me a squinty eyed suspicious look.  Besides, her sister can't eat most fast food.  Why would I treat bumblebee to a dinner out when she's been incorrigible?  Right.  I wouldn't.  Scratch that idea.  What about soda with her meals?  She won't touch it with a ten foot pole.
After talking to a nutritionist and doctor, I find myself wondering if by serving veggies and water when the kids were little I somehow set up a junk food deficiency.  Wouldn't that be a good thing?  I suppose that depends on if the kids eat.
What happens when I decide I can be as stubborn as she is?  Recently I stopped worrying too much about what she ate.  She was pulling these tantrums over food, where she'd sit at the table with a plate of food in front of her and crying because she was hungry.  I took my cue from her newest therapist and shrugged.  There was food, tasty food.  There was food available.  I saw some of it enter her mouth.  If she was going to cry about it, I wasn't going to stay in the same room. 
She lost 10 pounds.  And then was hospitalized. 
Hungry kids don't always eat.  At least, not enough to keep themselves going and healthy, even if you make sure the foods they need are readily available. 
Several thousand dollars later, we're no closer to an answer to picky eating.  Our recommendation is to feed her anything at all she's willing to eat, even if I have to go out at 2am.  But, don't become a short order cook.  Make one meal and if she eats, great.  Hungry kids, after all, eventually eat. 
Please tell me I'm not the only one who thinks that's conflicting information?