I finally figured this problem out. It has to do with permissions of all things! Right click on the folder that HandBrake is set to write to and choose "Get Info". Then at the bottom you should see "Sharing & Permissions". Click on the triangle next to that text if there is nothing displayed beneath that text. Then click the lock, enter in your password, then see if Administrators or your username are listed. If not, click the "+" and select Administrators or your username from the window that pops up. Then in the "Get Info" window, click on all of the names at the bottom until it shows the one you just selected from the other window. Change the "Privilege" to "Read & Write", then click on the gear and select "Apply to enclosed items". Click that you are sure, and then close the "Get Info" window. Then try HandBrake again on that folder and see if it works.