Integration of WP blog into another CMS

Is there any scenario where it is not possible to integrate a WP hosted blog into a separate domain?

I have a client who is telling me it’s not possible to point their WP hosted blog to their main website but I was under the impression that any website could create at the very least a subdomain such as blog.website.com, then create a cname record to point the subdomain over to their blog.wordpress.com site.

Thanks!