This claim is grotesquely oversimplified and misrepresented. Yes high cortisol could lead to adverse side effects including a diminished inability to cope with stress. However: low cortisol will have severe side effects as well including reduced testosterone levels (which will affect neurotransmitters including serotonin) and will affect igf1 release amongst other needed hormones.
I strongly recommend rhodiola rosea since it seems to be a smart adaptogenic - if you have too high cortisol if will bring it to normal and if you have too low the same thing will happen.
Not sure about ashwaghanda.
I think where maybe some of the confusion comes in is that we measure cortisol to measure stress, is that correct? Also so high cortisol effects the ability to recover and cope with stress? So unless you bring your cortisol down your essentially going to be prone to stress. I looked into Rhodioloa Rosea, it appears to be in the same class as Ashwagandha wihich is a adaptogenic as well.
Abnormally high cortisol is an indicator of high stress. What happens with time in these cases is that sooner rather than later cortisol production halts and they end up with abnormally low cortisol. People with PTSD tend to have abnormally low cortisol, although we would have guessed they have high cortisol.
The adrenals simply couldn't keep up and crashed.
I recommended rhodiola since it's the supplement that worked and helped me personally but ashwaghanda didn't. And functional medicine practitioners tend to recommend rhodiola as opposed to ashwaghanda - not sure why.