Unfortunately, there is never any hard proof that a book is in the public domain. There is only hard proof that a book is still protected by copyright.
It's the literal absence of the this hard proof that a book is still protected by copyright that places a book in the public domain.
When a renewal has occurred and a book is still protected by copyright, it's an easy matter to just locate and print out the renewal as proof. When a book hasn't been renewed however no renewal can be located...thus there is nothing to print! And of course, it's this absence of renewal record that places the book in the public domain. It's kind of a frustrating catch22 situation.
You can have a copyright lawyer conduct a search for a book's copyright renewal record and what you will end up with is a document that states "no renewal found" or something similar. The document itself is still not hard proof that a book is in the public domain, but rather, it's simply a report stating that they searched for a renewal but were unsuccessful in locating it.
In the unlikely event that you are ever challenged for your use of one of these books there are three things to keep in mind...
1) the burden of proof lies on the accusing party. they need to be able to provide valid proof that the book is still protected by copyright. If they do actually own a valid copyright to a book, producing proof of such should be an easy matter.
2) take the time to make sure you understand the process behind researching a book's copyright status so that you can communicate effectively as to why the book is in the public domain, i.e. no renewal can be located on file in the 28th year after publication specifically no renewal occurred in the years 19xx, 19xx, or 19xx. Full instructions for this are found in your Public Domain Treasure Hunter's Survival Kit. Sometimes, you'll find that another party falsely believes they own the copyrights to something and they need to be educated a little as to the truth of the matter.
3) Get us involved if need be and we'll be glad to help you assess the situation.