Hmmm, maybe, but first try locating that file via FTP and checking it’s permissions. Assuming a ‘nix server, the usual permissions are 644, but check some other file permissions where access is working, like wp-includes, and match what ever permissions they have.
Check the tinymce folder permissions too. Folders are typically 111 more than files, so usually 755, but as before, match whatever is working on your server.
Do you know if any server level security like mod_security is running? Sometimes it can decide to arbitrarily decide to lock out certain resources in a way that makes no sense.
There could even be some .htaccess rule that accidentally locks out a resource. Check any .htaccess files for such rules.
These are all typical reasons for inappropriate 403 errors. If they all checkout you may as well try a manual installation since I’m out of ideas. Be sure to completely delete wp-admin and wp-includes (NOT wp-content!) first to prevent any weird inheritance issues.