[dredmorbius]

Under civil law in the United States, the legal burden is not "irrefutable proof", but "preponderance of evidence".

If you produce copies of a letter with a given return receipt number indicated on it, the return receipt stub, and the received receipt, and the opposing party claims that "this could have been faked", then, unless your credibility is otherwise impeached, you have established a preponderance of evidence for your claim.