That... doesn't make sense. They can choose to publish or not publish whatever they want in their paper. The top people at a newspaper are literally called editors, and they routinely make decisions about what goes in and what does not.

This is more like a newspaper taking down specific old articles from a specific reporter from their website.

Happens all the time. Like, IIRC The Spectator (a hard-right wing publication) taking down a fawning article about Greece’s far-right Golden Dawn by Taki. Maybe I misremembered the specific piece, but I can’t find hide nor hair of it on the Spectator website, despite plenty of (broken) links to it from commentators.

It… does. They just remove the words before printing. It’s called an editor.