While it is true that you cannot be sure that it's because of your speech, a lot of stammerers are employed in jobs where they are required to speak, including myself. You have to stand out, if you show that you really couldn't give a shit whether or not you have a stammer and you just want that job because you'd be best at it, let them know that with your attitude. If they're employing less professional people instead of you, there you have the issues.