Yeah, that's not a problem at all.
Are you sure the burden of proof would lie on them?
I guess this is the core of what I was asking.
Would I have to wait to receive the certificate from the copyright office before I can publish the work to be on the safe side?
If it takes several months to get it, and if I publish the work right after I drop the envelope in the mail box, what stops them from copying it and filing themselves?
That's not a problem. The last time it happened I started getting angry e-mail messages from customers asking for a refund because I "sell stolen content that I stole from such and such."
If I don't hear about someone and my work then they are too small of a damage to worry about.