They allow sponsored content they're just really restrictive about it.
For example I couldn't wear my work shirt (with logo) during a 2 minute piece on a kids TV program. However, watch whatever is on on a Saturday night, guest appearance from some "star" and the host's question will be "so, you've got a [media product] coming out", with a promo image of the book/movie/CD/whatever. Or if it's a movie then they'll often show a short clip (aka advert).
If you watch a cooking show then it seems it's fine to promo a restaurant as long as it's high-end - here's such-and-such chef, fresh from his Michelin starred restaurant at Poshtown. It's quid pro quo but waiving [part of] an appearance fee in order to get publicity surely counts.
It's curious, some kids shows are all black-tape over the carton being used to make a craft project but then they have an "inside the factory" series which is a massive promotional piece - though probably not paid - for the companies with branding clearly shown. You might argue not "sponsored" but "we'll let you do this filming if you show our factories in a good light and keep our name and logo in the show" seems sponsored to me.
Makes you wonder though. The story about the million-dollar page is pretty interesting but there's nothing special about the Calm app, yet more than half of the article is about it.