The credit card may be the key. I've run into this scenario a few times when redesigning sites for small businesses, as JamesRyan said its not unusual.
Its also not unusual for managers to be unclear on the nuances between URL ownership, hosting and email hosting. Very simply:
URL ownership: You purchase the right to use a specific name as a destination for your website (somecompany.co.za) for a specified period of time.
Webhosting: Your website files are on a computer that serves them to visitors. Visitors find your website when they type in your URL if it is pointed to your server's numeric IP address.
eMail hosting Your emails come and go from a computer/server and are sent to your personal devices, most often with your URL in the email name (firstname.lastname@example.org).
Sometimes these 3 services are bundled and performed for you by one company, but not necessarily.
If the domain name and/or hosting are paid for with a company credit card, you'll know who you are paying, and can call and confirm what service they're providing. We've been successful reclaiming the URLs and hosting by contacting customer support for the supplier and proving that we are the people paying for the hosting.
Tenacity has been helpful to me solving these issues. Best of luck to you!