In order to earn the beta badge, you not only have to have signed up for the site during its definition stage before being launched, but you have to actively participate. This means asking and answering some minimum threshold of questions.
The numbers you are looking at indicate that at least 6262 people signed up ahead of time but only 2157 crossed the threshold on activity during the private beta phase and got the badge. The other 4000 something were slackers.
Honestly I'm not sure what the private beta stage was for SO since the process then was different, but presumably the badge got retro-actively awarded at some point with similar credentials such that early participants received it (on Sept 16th, '08 apparently).