But don't take my word for it, listen to the federal government:
"Copyright protection subsists from the time the work is created in fixed form. The copyright in the work of authorship immediately becomes the property of the author who created the work. ... The way in which copyright protection is secured is frequently misunderstood. No publication or registration or other action in the Copyright Office is required to secure copyright. See the following note. There are, however, certain definite advantages to registration. See Copyright Registration on page 7"
"Registered works may be eligible for statutory damages and attorney's fees in successful litigation. Finally, if registration occurs within five years of publication, it is considered prima facie evidence in a court of law"
I think you may be misreading that clause. What they are saying is that if the works are registered, you may be able to sue for statutory damages in addition or instead of compensatory damages. This does not mean if the works are not registered, you cannot pursue legal claims, merely that you're limited to compensatory damages. Likewise, they are not saying you cannot prove that you own the copyright unless they are registered, merely that copyright registration effectively shifts the burden of proof.
https://en.wikipedia.org/wiki/Damages#Compensatory_or_expect...
https://en.wikipedia.org/wiki/Statutory_damages_for_copyrigh...
The symbol it's about being explicit about who owns the copyright. The owner of the copyright can then decide which license to use. Or not use any. But choosing not to license doesn't make you lose the copyright nor makes the creation free(libre).