SELinux can be tricky to configure with MySQL
Fedora and Red Hat are using SELinux (see in /etc/sysconfig/selinux if SELINUX has a value of "enforcing"). I had installed (2 years ago) MySQL on RHEL 5 and I had to tweak SELinux so it would play nicely with MySQL.
If it is not an ACL permission deny (like sugested by Barry Brown) then try to look if by setting SELINUX to "permissive" (and rebooting) this does not solve your problem. Setting SELinux to permissive will not deny a process the access it requests, but it will be still logged. So if SELinux is the culprit, you will get informed in the logs and MySQL will anyway be able to start.
If it did solve your problem but you want to keep SELinux activated, look for SELinux+MySQL+Fedora, I had found plenty of resources 2 years ago on this matter. Things might have changed since that time and might depends on MySQL versions, etc. So I cannot give you better advice than pointing you in the right direction. :)