We have a number of neighbors who hunt deer in our timber every fall. This means that we have access to a fair number of deer carcasses, delivered fresh to our farmyard. Now you may well be wondering what this has to do with our chickens.
While we don't feed any animal byproducts, chickens (and other poultry) are actually not vegan animals at all. All of our birds will hunt and eat small mammals, amphibians, etc. Hens in particular are excellent hunters of mice and other small creatures, spending many happy hours wandering the barn yard looking for prey.
A few years ago we started experimenting with ways to boost our birds' protein intake to help them keep laying through the winter. One of the best ways we've found is to provide them with a fresh deer carcass that they can strip clean. Even after it freezes they will happily peck at it all winter, keeping them healthy and busy.
All this to say, don't pay attention to any eggs that say they're from vegetarian birds if you want eggs from birds that are truly free-range. Any free-range bird has been out hunting, but it's totally valid to find out what sorts of animal products are being direct fed to the flock.