Rescues don't have to be and probably won't be picture perfect. Stress and Rescue (I am SSI also so I recognize the course name) places its emphasis on exactly what you are asking. I can't speak for the Rescue courses in other agencies, but judging by the fact that Charlie's response reads almost exact like my Stress and Rescue course, I assume that they do as well.
The emphasis is how to prevent and identify stressors BEFORE they turn into a full blown panic and how to minimize the stress in dive planning.
Yes, they do make you learn how to pull up a panicking diver who wants to grab your air hose (my course went with my DiveCon, so I am expected to learn that) and how to deal with an unconscious diver on the bottom among other things. It is FAR EASIER and MORE EFFECTIVE to catch most of this stuff as far back as the breakfast conversation (if possible) in the morning than once panic starts underwater.
A personal experience will illustrate my point:
On my AOW class, we were on a dive in a local lake. There were three students and an instructor. My dive buddy was a student who had been buddied up with his best friend for literally every dive through Open Water. I am single and had "pick of the draw" dive buddies for every dive through Open Water and had about 10 more dives. I was also planning on taking Stress and Rescue and had already purchased the tape and book. I had studied both. The newest diver was a young lady that I had certified with who hadn't dove since her open water. She was "very light on insulation". She and I were alike in that regard and were doing our drysuit certs as well. "Laurie" (I'll call her that for convience) was buddied with the instructor.
About ten minutes into the dive, I noticed that Laurie was looking a little worried. I couldn't tell about what, but her movements were a little too quick. My dive buddy was doing all right and he slipped up by the instructor to check something out (I can't remember what). I hung back. Sure enough, I see "Laurie" looking around like she is trying to get the instructor's attention. Then her eyes go grapefruit wide. At this point, she starts reaching for her secondary regulator. This all happens quickly enough that alerting either of the other two is not going to happen.
I give her the "up" signal and prepare to share air if needed. She breathes out of the secondary regulator on the way up and we do a controlled ascent. But she settled right down the minute that she knew that she had my attention. She mentions that her primary was breathing a little wet and that the water coming in bothered her. I don't know enough about regulators to help with that then (Over the weekend it turned out that the regulator had a leaky diaphram.), but I knew enough that the instructor would note her abscence and be up shortly. In what seemed like forever, but was probably only a few minutes, the instructor came up checked out the regulator, and we found it good enough to continue the dive.
My point: it was far easier to recognize her getting stressed and get her to safety than it would have been if I had been watching her flail around in a full-blown panic. She was close. The minute the eyes get that "wide open grapefruit" look and movements start getting that quick, I have since learned from experience, that nothing good will happen if it continues and there isn't much time involved.
At the very least you will know what to look for to start thinking about getting people to safety instead of continuing the dive in the manner that started. That class is also why I practice good health habits myself. It is easy to help prevent myself from being panicked if I am comfortable in myself.