I found this workaround, should work until Apple/Mathworks issues a patch:
Download the Apple Java SE 2013-003 update (no longer on the Apple website but I found this link:http://apple-java-for-mac.en.softonic.com/mac/download)
Then download and install Pacifist http://www.charlessoft.com
Use Pacifist to open the Apple Java package and install using the install option of Pacifist.
Your Java SE should be downgraded to where it was prior to applying the 2013-004 patch. This worked for me, matlab is functional again.
JSource: http://www.mathworks.com/matlabcentral/answers/79489-java-1-6-0_51-breaks-matlab-2012b-and-below
Author: http://www.mathworks.com/matlabcentral/answers/contributors/4383739-julien-aubert
If you find this useful, please visit the source link and upvote Julien's answer.
For anyone who's curious or concerned, Pacifist is just a shareware (free trial) tool to let you install older versions of applications, bypassing any "safeguards" Mac OS has in place. The whole process was simple, easy, and much faster than Googling for other options (which I also did).