So, I set out to find the answer on Skype forums. Here's where I found the answer.
#1. Run "LD_PRELOAD=/usr/lib32/libv4l/v4l1compat.so skype" at the command line and test the video in Skype again.
(If that gives you an error, you may need this instead: LD_PRELOAD=/usr/lib/libv4l/v4l1compat.so skype)
#2. Create a new file in your home directory called skype. (/home/user/skype)
#3. Edit the file skype and put the command from #1 in it.
#4. Run "chmod +x skype" in order for the script to be executable.
#5. Edit the skype launcher and change the command to /home/user/skype. Substitute user for your user name of course.
Now Skype video will work without the hassle of running an archaic command from the terminal.