You're somewhat right. But the primary thing that makes perceived eye lens flares so distinct is not their pattern so much as that they're dynamic, because it's nearly impossible to stay absolutely still; your eyes, head, body, eyelids, are all moving somewhat, and that affects the appearance of the flare. There are other factors too, which make it nigh impossible to simulate a perceived vision lens flare with current real-time gaming graphics. That is one reason why it is more common in many cases for game devs to try to simulate flares from video cameras, for these are much more static and predictable. The only case in a game where I've seen any flares that come close to showing what the eye sees is in Mass Effect 3, where some flares in the environment were dynamic and changed depending on your viewing angle. No doubt this sort of effect will become more common in the future.
I saw a great demonstration and explanation of this very phenomenon, the physics behind it, and realistic ways of rendering human eye lens flares in CG on a web page somewhere, but I can't find the link right now.