I think our webhost is a bit special. Well, at least I'm hoping they are wrong in what they are telling us.

We need Centova stats to work, but they are saying that it cannot work if Centova Cast and the Shoutcast stream are on different servers.

Is this true? Does Centova cast not use some sort of database on its own or something like an SQL?

I'd love to know how to get it working where I can let them know. The stats would be greatly beneficial to us.

Thanks for your help!

Yes, that is correct. At the moment statistics will only work if Shoutcast is hosted on the same server.
That's because statistics rely entirely on the information sent by Shoutcast and since it is hosted on a different server, no data is sent.
In the upcoming version of Centova Cast (v3) this will not be the case anymore and statistics will be generated regardless of where the Shoutcast server is hosted.

Although to clarify what AlexiuB said, part of Centova Cast still needs to be installed on the same server as ShoutCast DNAS.  You just don't have to run Shoutcast DNAS on the same server as the Centova Cast web interface.  Obviously CC needs access to ShoutCast DNAS' logs in order to process them, so it can't magically procure log data from a random remote server.