They actually own the copyright without paying anything. However if they want to sue someone based on copyright they have to register with the Copyright office.
This is per the
US Copyright Office's FAQ
Do I have to register with your office to be protected?
No. In general, registration is voluntary. Copyright exists from the moment the work is created. You will have to register, however, if you wish to bring a lawsuit for infringement of a U.S. work. See Circular 1, Copyright Basics, section “Copyright Registration.”
Why should I register my work if copyright protection is automatic?
Registration is recommended for a number of reasons. Many choose to register their works because they wish to have the facts of their copyright on the public record and have a certificate of registration. Registered works may be eligible for statutory damages and attorney's fees in successful litigation. Finally, if registration occurs within 5 years of publication, it is considered prima facie evidence in a court of law. See Circular 1, Copyright Basics, section “Copyright Registration” and Circular 38b, Highlights of Copyright Amendments Contained in the Uruguay Round Agreements Act (URAA), on non-U.S. works.
Also worth noting that it is only $35 to register for a copyright online.