They’re not wrong. In countries with implicit copyright (those following TRIPS[0]), barring any license to the contrary, you have no right to the copyrighted work published online. In other words, unlicensed code is “all rights reserved, no exceptions.”
There are numerous rights and exceptions. Which exceptions apply vary by country and I can't speak for all countries, but virtually nothing in copyright law is strictly without exception. Unsurprisingly there's no shortage of people eager to convince you otherwise.
As an aside it is very strange that so many people derive their understanding of copyright law from various international treaties. These very rarely come into play in actual U.S. copyright cases and have little influence over the way courts interpret the law.
[0]: TRIPS Article 9 Section 1: https://en.wikisource.org/wiki/Agreement_on_Trade-Related_As...