Interesting question. Not sure it could be answered, but does it present a catch 22. I mean if their ego tells them that they are "enlightened" then are they? or are they suffering from the delusion of what they see themselves as, or what they want to be seen as?
It's hard to separate these questions from the western Christian mindset. At least from the Zen perspective, your question makes no sense. To be enlightened is to see things as they are; there's no contradiction in seeing yourself as you are seeing things as they are. If you see what I mean.
The idea that this might be egotistical comes from a western idea of hubris and humility that simply doesn't translate.