I found out that to pull the actual database file (my_database.db) you have to use chmod on that specific file in the adb shell. So you need to explicitly define the path to the database you want to access.
For example, if the database file were my_database.db and the application package was com.example.database, you would need to call the following:
1) In cmd type: adb shell
2) Type: su
3) Press "allow" on the rooted phone
4) In cmd type: chmod 777 /data/data/com.example.database/databases/my_database.db
5) Go to DDMS in Eclipse
6) Navigate to the my_database.db file and select it
7) Choose "pull a file from the device" and choose where to save it
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…