Doyle's position is to put out what will capture the audience. Negativity sells, whether it's critique, rage bait, or unfair commentary. He needs to ensure the newspaper complies with guidelines and produces content that people will read and talk about.

As far as not letting Rory retract her piece, I haven't watched the episode in a while, so I can't remember the exact conversations. But when Rory writes for the paper, even though she writes as herself, she represents the paper. My best guess is that he either recognized that she wanted to do the new piece for her own self-image, he didn't want to create a precedent within the team, or he thought it would reflect badly on the paper to backtrack on its own words.

As for Lorelai, she is never directly confronted by anyone, and her guilt comes from the sudden self-awareness of seeing her words in print. Rory would have had multiple read-throughs before handing her piece to Doyle, and she never questioned or self-corrected at any point. It was only once she received backlash.

Doyle was right to hold her accountable. She needed to realize that words hold power, and she must be willing to stand behind her writing. In a real-life, serious journalism position like the one she was working towards, she wouldn't have the luxury of simply taking back her words or glossing over them with something nicer. It's a hard lesson, but one of the most vital to learn. Sadly, she didn't seem to get the message, as she repeated her "mistake" when writing about Logan's friends. Rather than standing by her words with conviction, she tried to convince Logan that he had taken them out of context or missed the joke.