Except for the API (mentioned by @Gilles), there is no read-only access to a private beta because the the site itself is not finished, yet.
If you let the public into a site still under construction, you run the very likely risk that they'll see this mess and say "This site royally sucks, I'm outta here!" …and they will never come back.
The purpose of a private beta is to finish building the site prior to opening it the public. I often talk about the empty restaurant syndrome where it isn't very appealing for passers-by seeing a bunch of empty seats. But more than that — In the opening days, you don't want people wandering in off the street when half your ceiling tiles are still laying on the floor, mistakes all over the menus, and half the staff walking around with mops and buckets.
So we restrict access to the site to all but a select few who agree to help us sweep up a bit and start filling those seats for opening day. There's nothing about read-only that's going to keep some over-anxious blogger from announcing "Hey, the XYZ site is open, go check it out" …only to be seen by thousands while still under construction.
The private beta has to be restricted to those who sign up for the process. Making it read-only does not mitigate the reasons it is a private beta in the first place.