Associating domain with existing WordPress site

I am setting up a new WordPress site for an organization. When it is ready, we plan to transfer the existing domain name of the organization to the new site.

The hosting service, which is usually expert and professional, tells me to be cautious about this. Their support says, “WordPress hard-codes the domain name into its URLs, so it is best for the domain’s DNS to point to the server while you work on it.” They advise transferring the domain to the new site before we start developing it. Of course, we cannot do that because the domain name is currently used for the old site, a non WP site.

This information sounds strange. Is it true? Can someone clarify what it is all about? Specifically:

– Where precisely does WordPress hard-code the domain name?
– What kind of problems will we encounter if we develop the site first and then transfer a domain to it?
– Is it possible to fix the problems?
– If WordPress hardcodes the absolute URLs of the pages, it would be impossible to transfer a WordPress site from one host to another. But I understand that WordPress sites are easy to transfer. What’s going on?