This is easy to understand. Most of these media-shy liberals draw their paychecks from institutions that depend on money collected in offering plates in parish pews outside the urban East and West coasts. Also, there are conservatives who worry about media coverage, for reasons that are very similar to those of the establishment liberals. This is easy to understand. They know that laypeople have been known to read newspapers and then react.
Media coverage causes heat.
This causes debate. Debate causes pain. The larger the debate, the more pain. Many establishment conservatives fear that the pain of open debate will hurt the church. They may be right.