An excellent suggestion and excellent advise.
However, Log::Any isn't available through either the default CentOS repository or the RPMForge repository. Version 0.15 seems to be what's installed by default with the OS. I just took a step back and reinstalled the OS to a VM to start fresh. Having only installed the RPMForge repository, I get the same error with "yum install perl-HTML-Mason".
Perhaps HTML::Mason doesn't work on CentOS 6.4? I'm not sure how to force it to install without the dependency check on Log::Any. That's the next thing I'm looking into.