I'm sure that if we could collect cortisol samples throughout the unfolding of a day, be it a normal day or even a wonderful day, we'd see these levels moving up and down.

I'm not sure that dogs read our emotions, so much so as they feel them. And I'm not sure that the way they feel them, is parallel to the way we make quite high conscious experience of them. What I am sure though, is that there is some form of emotional contagion between our 2 species.

I don't think that a social species, needs to be "trained" to calm the pains and stress which result from emotional contagion. This is certainly my biggest disagreement with your colleague.
No one thoughts dogs to get rid of excess saliva, by licking it, when they feel stressed. No one teaches them to move away from a source of stress when it becomes too intense.

A therapy dog which would not have the ability to self regulate herself in regards to this, shouldn't be used as such. Pal of mine made a bad fall, hit his head hard on the floor, and stood back up, dizzy, suffering from a concussion.

His dog took a full 24h to recover from his personal experience of this trauma. You can't train a dog to avoid that. Not every human could be a therapist neither.