The responsible thing is to use caution and discretion when introducing any animals to each other---even ones of the same species. You're right that some* species combinations should never be attempted, but cat plus rat is not among those IMO. The potential for interaction should be judged cautiously on an individual basis.

Most people understand that not all dogs and cats can be trusted together. That's why we don't need disclaimers on videos of dogs and cats being cute together. Cats + rats are only slightly lower than dogs + cats on the compatibility spectrum. I think a disclaimer would be appropriate but I also believe it's not necessary here.

Rats are my favorite animal. I've had thirty-one in my lifetime. I never once placed one of my rats in the same environment as my cats, but nevertheless I had a rat become good friends with my kitties (hence my investment in this topic). It was something that developed naturally from his curiosity and aggressive affection. I very gradually expanded his freedom of movement and interactions. Like the cat in that video, my cats were intelligent enough to recognized him as part of the family. I know that it wasn't for a lack of prey drive because I found dead (wild) rats in the garage a couple times.

*Including Rodent+Bird, Rodent+Lizard, Mouse+Rat, Hamster+Rat, Dog+Rodent