No. There's clear definitions of what is to be called a domain and what a subdomain. Contrary to what you say, Google*com is NOT a subdomain, it's a second-level-domain under top-level-domain dot-com. domain*co*uk is a domain by convention, as the UK has introduced a second level in their top-level-domain dot-uk. Domain*co*cc is a subdomain, as no official convention about a second level of the top-level-domain dot-cc exists.
To sum up: whether to call an URL a subdomain or not does NOT depend on the "scope of mind"