Well, after some struggling, what worked for me was completely removing the current JDK, as described here:
sudo rm -rf /Library/Java/JavaVirtualMachines/jdk1.7.0_80.jdk
sudo rm -rf /Library/PreferencePanes/JavaControlPanel.prefPane
sudo rm -rf /Library/Internet\ Plug-Ins/JavaAppletPlugin.plugin
sudo rm -rf /Library/LaunchAgents/com.oracle.java.Java-Updater.plist
sudo rm -rf /Library/PrivilegedHelperTools/com.oracle.java.JavaUpdateHelper
sudo rm -rf /Library/LaunchDaemons/com.oracle.java.JavaUpdateHelper.plist
sudo rm -rf /Library/Preferences/com.oracle.java.Helper-Tool.plist
Then installed 1.7.0_21, which was downloaded from here.
Now java -version prompts:
java version "1.7.0_21"
Java(TM) SE Runtime Environment (build 1.7.0_21-b12)
Java HotSpot(TM) 64-Bit Server VM (build 23.21-b01, mixed mode)