While probably true the main reason is they are no longer making eggs when they are sitting.
If roughly one third of their feed intake goes towards making an egg; say normal is 100 grams of feed eaten a day, and say they lay eggs of a weight of 40 grams, then in theory they can eat 40 grams less a day and maintain their initial body weight.
Ideally, a hen should put on a little weight when sitting. Once the chicks hatch she won't get to eat much for a few days because everything she finds will be eaten by her chicks. I a hen hatches six say, that's a lot of mouths to feed and a lot of energy expended finding food for the chicks.
I think, when people post that their hen lost weight when sitting, at least some have fed the hen at the nest site. I don't know if it's true, but I've been told that hens that eat when sitting don't eat as much and don't digest as well because of the pressure on their gizzard and crop when sat on the eggs. A hen roosting on a bar distributes her body in a different manner. Plus, all the broody hens I've watched trance and if the trance isn't properly broken they don't eat properly.
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