Cats and dogs (in my experience) will stay very close to you when you are sick, sad or upset or if they perceive that anyone means you ill - even of thought.
At the first sign of an argument, my kitty cat will come right to my side and place herself as a shield between me and the world. If I should cry, she will come and sit purring right by me. If my husband is sick, I will know where one or more of the furry ones' will be. Grand-doggie will do do the same, or bark until he's sure nothing will harm me or those he loves. If ever not feeling well there is always an almost palpable beam of pure love emanating radiant energy into my spirit directly from my kitty cat. As close to me as she can get. I often wonder aloud, how such small creatures as kitty cats and a tiny pom-pom can exhude so much good energy without depleting themselves.
Without a doubt, they can tell when something is going on health or spirit wise, and their first instinct is to get close and to offer their best gifts: warmth, love, companionship.
It is sad to hear such damaging comments about animals as it only creates more irrational fears. The world belongs to them as well, and we should be their protectors.