I think you might need to use lstat instead of stat.

At the bottom of the stat docs, it says:

To get status info for a symbolic link instead of the target file behind the link, use the lstat function.

And in lstat:

Does the same thing as the stat function (including setting the special _ filehandle) but stats a symbolic link instead of the file the symbolic link points to. If symbolic links are unimplemented on your system, a normal stat is done.