Fedora 16: "Permission denied: file permissions deny server access"
Solution 1:
If memory serves, you probably need to run chcon -R -h -t httpd_sys_content_t /var/www/html
This recursively sets your content directory to the proper context for Apache.
Solution 2:
This file permission issue is, as you expected, due to SELinux. Its rather complicated, but the good folks at CentOS have put together a pretty good wiki to get you going. In short, you can either disable SELinux (totally bad idea), set it to permissive mode (slightly less bad idea), or work with SELinux. Since the wiki goes over the details in a fairly succinct fashion, i will keep it DRY and let you read the wiki.
I fixed mine by copying the files into /var/www/html and then restoring the default context for that folder using:
restorecon -Rv /var/www/html