I am not seeing what you are seeing under Appearance. Do you have Platform installed somewhere or are you just reading their publicity stuff on their WordPress.org page?
What I see is wp-admin -> appearance -> Platform Settings. AND I cannot see a way to add a custom header in spite of what they claim on their theme page.
You are totally correct that they claim you can set a custom header. Platform even comes up on WordPress.org theme searches as a theme when you have custom-header as a required tag. But I do not see a way to set a custom header unless you buy their full package which is way more than I need and amazingly expensive. (One year including the forum comes out to $245!!)