Hi Donna
I am not a lawyer but your PRO should be able to give you something more definitive. Meanwhile I'll refer to a few sources.
http://www.teachingcopyright.org/handout/public-domain-faq
Publicly available and public domain are not the same thing. My understanding is that to be considered public domain either copyright must have expired or it is an item where copyright does not apply, such as a title, or a short phrase, a concept or idea etc.
Free doesn't enter into it. Where free can have bearing is where a work can be considered published or not published.
Public display does not constitute a waiver or transfer of ownership rights.
Ownership of a copy does not constitute a transfer of ownership rights. What you do gets are rights regarding the copy, not the original work, even then those rights do not extend to alteration of the work of the creation of derivative works by any means.
"Two General Principles
• Mere ownership of a book, manuscript, painting, or any other copy or phonorecord does not give the possessor the copyright. The law provides that transfer of ownership of any material object that embodies a protected work does not of itself convey any rights in the copyright."
http://www.copyright.gov/circs/circ01.pdf
Either your work is considered published or it isn't, but either way copyright ownership is established on creation of a work, independent of whether it is registered or not. For your work to be used as described you would need to actively give permission to the entire world to be able to use it in that way, and even then you would retain moral rights. Not all countries would even allow that.
If what this guy asserted was true nothing that was free (99% of the internet) would be protected by copyright, that means none of what any publicly viewable website offers would be covered including newspapers, books, nothing at all.
From the Us gov doc above you will find
"Notice of Copyright
The use of a copyright notice is no longer required under U.S. law, although it is often beneficial."
That I understand mainly has bearing on "innocent infringement" which this man's communication already proves it is not, it is merely ill-informed.
"Who Can Claim Copyright?
Copyright protection subsists from the time the work is creÂated in fixed form. The copyright in the work of authorship immediately becomes the property of the author who cre ated the work. Only the author or those deriving their rights through the author can rightfully claim copyright."
Out of interest, by removing your copyright notice, by altering it, I understand he is committing a crime (page 163)
http://www.copyright.gov/title17/circ92.pdf