But News is very much commercial speech as well, if not moreso than political.
Advertising, product labels, or advertisement signs are examples of commercial speech.
As for the actual content and their right to say it? It's their right. It's protected. But selling snake oil as a cure for cancer? That's the issue.
But in all seriousness, freedom of the press doesn’t imply it has to be purely factual or completely objective. The press is free to analyze, opine, ridicule, and rile their audience however they decide to. And they can even call it “fair and balanced” or tell me it’s “fit to print” if they want to, because these are subjective terms describing their opinion in a field expressly exempt from regulation.
In other words, about as far from selling a fake cure to cancer as you can get.