I don't know what "eligible" means in that context.
Obviously it means something very specific and in concordance with some written contract or some law. It is a reasearch project to find out what that language means. Let me know what you find out.
One might just as well scream, since the IRS doesn't think my daughter is a qualifying member of my family, "who are those bastards to tell me my daughter is not my daughter???!!!"