I hope the issues aren't a manufactured problem by the site provider to try to force you to upgrade what you pay for the server.
BTW, I know many people who hire professional website creators have problems. I hope you make sure it is done in a way you can easily maintain it, without their help. KISS. And that you, not the commercial firm, owns all copyrights, licenses, and site registrations.
This particular paranoia is justified. I've known business owners and organization managers who ran into these kinds of issues. Website creation and management is poorly regulated at this time.