I guess it depends on if you want the database hosted with dynamic queries or just static pages from the database data.
I'm not sure about your "reasons". If you HOST a database (any kind, MySQL & FileMaker included) and use it for web publishing, you can put restrictions on it, but it's still "out there" and subject to external factors for sure!
Research IWP (Instant Web Publishing) with FileMaker if you want to host the database, otherwise you'll need the php (or other web app) skills.
If you know how to create HTML, you can use FileMaker's calculations to create static HTML pages from the database contents. Then just export the "text" and name the extension whatever your website requires. Upload the file(s) to the website and you are "good to go". If you have a site that does not require queries and does not change often, this can be an acceptable alternative.