In private browsing mode the site won't have access to the cookies stored in the browser that it's been using to keep track of the number of "free" articles you've read. In addition, some news sites will selectively disable the paywall for certain referrers, especially search engines and social media sites, to strategically gain hits. So when you do what the original comment suggested, you appear to their site as someone who has never visited before and came from a Google search — in other words, they don't want your first experience with their website to be a paywall.