I've never had an egg eater,including that hen, other than the opportunistic kind.
I had a run of "rubber" eggs when my girls started laying - but they always got dropped on the coop floor, then would break and inevitably get eaten. If they weren't broken I would toss them into the run for the hens to eat. I also give them shells practically whole without baking them...
My personal thought about egg eating is that when there is too much light in the nest box, some of the ladies get curious and start pecking (ever seen them with a mislaid egg in the run?) and if they break them that way it could be habit forming, should they not have enough other stuff to keep their minds occupied. With a good dark nest they tend to do their business then leave, in my observations.
I also suppose diet could come into play, chickens are good at finding what they need so in a minimum protein situation they may turn to eggs.
I have however had a (not broody) hen try to eat a 3 day old chick... She's a nasty hen though and regularly kills frogs about that size so I shouldn't have been surprised!