The Lodestone needs to fine-tune their stuff :( They show the exact same thing we do (the level 4-9 Wild Dodo drops it... ) http://na.finalfantasyxiv.com/... ...but that's clearly wrong, based off of what you say.
Sorry we had incorrect info :( I try to keep shit as accurate as possible, but SE makes it impossible sometimes!
EDIT: Your comment also inspired me to look into our code and figure out why we were showing so many Results for something dropped, when there should only be 2 or 3 (for this page, anyways).. cleaned up the regex a little to narrow down the list :D So NOW, it should ONLY show exactly what mob drops something. (We also had the level 4 mob listed as dropping the egg, because SE on the Lodestone did, but I removed that)