I think you’re right about the server rerouting thing.
You can do this with .htaccess rules. From the top of my head, this might work:
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^ index.html [L]
Simply create a file in the htdocs folder of your website with the name .htaccess
with the contents above, and it should work.