The issue here may be that, while we think we know what the word "website" means, there is no technical definition for the word. So when you were talking to a provider, different people may have thought about different e techniocal approaches to what they thought you wanted to do.
For example, for a domain to resolve to a group of documents on a server, it needs an IP address. You can serve many domains from one IP address, or you can serve just one.
You've used the word subdomain. Normally this means an address like one.example.com and two.example.com. I notoice that you still want all three domain names to be usable - and apparently point to unique content, not just three different addresses to view the same content. This seems to mean that subdomains is not exactly what you had in mind.
So, I'd suggest you focus in on what it is, exactly and technically, that you hope to accomplish. Then, whether any particular provider will accomodate you and save you money depends very much on that business.