A commercial running on a channel doesn’t constitute the network sponsoring or promoting something. Ads are often purchased irrespective of what they stand for.
Also, not all ads are purchased by the network. I can’t remember the exact number but it was close to 60% were purchased through the satellite or cable provider, not the network.
So Fox News couldn’t deny the commercial, even if they wanted to? Sorry, I’m not familiar with how ad purchasing works.