To clarify further...
File extensions in anything UNIX / LINUX based, for the most part, DO NOT MATTER. Windows is STUPID and meant to be user-friendly, and thus uses file extensions to determine what to open how and how to use what and such.
BUT for most Unix / Linux programs, INCLUDING PHP / JAVA / PERL / ETC. the file extensions usually do not matter. You can include, fread, parse_ini_file, etc. anything with PHP. In fact, you're regular PHP files ( the ones that the user requests and views ) don't need to have the .php extensoin at all. They could be .htm. Or .php3. Or .jsp. Or .asp. Or ANYTHING AT ALL! You only need to tell Apache ( or whatever web server you're using ) that it should pass that file extension to a PHP module / executable before sending it to the user.
From a security standpoint, you really should never use .inc files, because of the problem you've found. MOST Apache installations treat .inc files as plain text, and MOST people don't have the permissoins or know-how to change Apache to make it treat them as PHP.
I've found a better solution is often to use filename.inc.php. That way I still know its an include file... but its a little bit safer.
On another note, if it has database connections nad passwords and stuff, try and store it outside the www root, so that the public can never request it anyway.