Please explain, why your SSL test requires an intermediate cert. Some small CAs issue certificate signed by their root. So the chains have their root and issued certs only, which is AFAIK possible. Your SSL server test reports an „Incomplete chain“ there.
Moreover, I have noticed, that CA roots are not supplied by the web server; instead they are read from CA itself.
However, if I use the EAS-MD program, it reads all the chain from web servers, 2 or 3 certs in every chain.