@JDnoble18 As George said, permissions look fine. Now that I think of it again I can imagine you ran into an issue where the installer would mess up with a link to the web root directory. Please run the following commands and post output here:
grep FOG_VERSION /var/www/html/fog/lib/fog/system.class.php
grep FOG_VERSION /var/www/fog/lib/fog/system.class.php
ls -al /var/www
I just tested kernel update on FOG 1.5.9.49 and it works as expected. So it does not seem to be a general issue.