I've rtft and it doesn't seem established to me.
As a mother of a very slim child who eats a lot and as an ex child carer what strikes me in your posts is you seem to want them to be eating 'healthy' food as in low fat, low calorie.
Growing children need fat, calories and as has already been pointed out more protein.
Ok they don't like houmous, what about taramasalata, guacamole, tzatziki, cheese or sour cream based dips? I'm assuming school and home = full fat milk cheese and yogurt? But how much?
But yes mistaking thirst for hunger can happen too but also if it's school holidays are they more active than usual? My dd more active in hols as she then has time for swimming, cycling and walking. When younger (she's 15) would have been running round at the park too.
Thinking back to when she was same age she'd have ready Brek or cereal, toast with butter and fruit spread plus fruit and milk to drink. Lunch was a hot meal plus pud at school, after school toast and fruit at after school club, plus couple biscuits or small cake (home made woman who ran it loved baking) dinner pasta bolognese, stir fry with noodles or cous cous, slow cooker dinner with potatoes of some kind with butter added to hers, soup n bread for supper.
Now admittedly she's not a fan of choc n quite fussy about cakes and sweets (I know what kid doesn't like choc!!) so no excess calories to worry about.
She's always been a good drinker which helps too, mainly milk or water but sometimes juice.
She's 5'6" and a size 6 currently and worries about her weight...as in she hates being skinny! Means she's not as developed as her friends.
Offer drinks if that's preferable but maybe milk instead of water, also check with someone maybe on portion sizes/nutrition balance?