Just to clarify:
There are two ways a new member can arrive. The referral field will be visible or hidden, depending on how the visitor arrives -
1. Visitor has heard about the site via word-of-mouth, and arrives without an attached referrerid. The field is VISIBLE. If visitor wishes to credit his oral informer then this is possible.
2. Visitor arrives at the site via a referral link sent to him/her by an existing member (with attached referrid). The field is INVISIBLE. The original referring member will be credited with the referral - even if the visitor would like to give the referrer credit to someone else, or simply give credit to no-one.