I think the public list is complete. If I understand it correctly, there's a separate private list (which includes email addresses) which is also complete, with the exception of your email address if you have not opted into sharing it.
Public list isn't complete as it only contains entries for those who have entered a BTC address to be published. So, e.g., if an asset is imported from GLBSE and shares assigned to email addresses with no existing account then there won't be any BTC address published for them (as there isn't one to publish).
Unless that's somehow changed recently - last time I checked listed shares for assets were (in some cases significantly) below those shown as outstanding.
Using BTC addresses rather than email addresses gives some degree of anonymity - but at the cost of ease of use and (more importantly) completeness.