How do I use time machine to access system files like /etc/hosts?
For OS X 10.11, El Capitan, the steps are:


Open Applications > Time Machine; or use the Time Machine menu bar item and select Enter Time Machine.
Reveal the Go to Folder sheet within Time Machine using the key combination: Command + Shift + G.
Within the Go to Folder sheet enter the path /private/etc and select Go.
You can now browse your back-ups of /etc/ and restore files as needed.