He did not say "before making copies". I watched that segment, and he did not say that. Now, he didn't make it clear that he had made copies in the segment, but in other venues he did assert that copies were made.

UPS also acknowledged that the package was indeed opened and the contents missing (though they did find them later).

The point, as he admitted in a text to journalist Roger Sollenberger, was that he was convinced that someone was monitoring his texts. That may be paranoid speculation, but it is not a lie.