Jeffries hammers this point home eloquently in his book where he states that "the failure to differentiate between physiologic and pharacologic effects has been a major factor in the confusion regarding the clinical value of these agents. When it was found that a normal replacement dosage for an adrenalectomized patient was 35-40 mg of cortisol daily, it became evident that dosages above this level were in excess of physiologic requirments." 
In his book Jeffries points out that, when they first studied cortisol - actually hydrocortisone which is metabolically downstream, i.e. the body converts cortisol into hydrocortisone - they were giving large dosages of 100 mg or sometimes more. This would miraculously cure many diseases from arthritiis to lupus, etc. However, it would often cause side effects. The solution, of course, was to lower the dosage to more reasonable levels. In Jeffries experience, if one does not give these overly large dosages of hydrocortisone, side effects are virtually absent:
"Other patients in our clinics have received small, physiologic dosages or cortisone or cortisol for various conditions that will be described later, totaling over one thousand patient years of experience. Other than an occasional incidence of acid indigestion, usually resulting from taking the steroid on an empty stomach, or a rare instance of a patient being allergic to an ingredient of the filler in the steroid tablet, no undesireable side effects whatsoever have occurred." 
Patients, as far as I know, are always given HC, or hydrocortisone, as Jeffries advocates, and not straight cortisol. This works out better, because our bodies convert cortisol to hydrocortisone anyway.
CAUTION #1: Ray Peat and others beg to differ with the idea that 30-40 mg of hydrocortisone is okay: ""The doses they prescribe as "replacement" are much more than the adrenals would produce, so they in themselves are diabetogenic. William Jefferies told people that, since the adrenals produce 20 mg of cortisol per day, they should take 30 or 40 mg, as a replacement dose, because only half of it is absorbed. They
got fat faces quickly. Using pregnenolone, they were able to taper off the cortisol in a month or two."  Some commentators also have concern with osteoporosis and other issues in the 30+ mg/day range. See my page on
How to Increase Cortsiol for details.
CAUTION #2: There is a common alternative methodology to raise low cortisol: pregnenolone. (HCG may also help some men.) This works (often but not always) in men with low progesterone and low cortisol. I found myself in that position and pregnenolone really helped, something I discuss here:
My Pregnenolone and DHEA Experience. However, this approach will not work for everyone.
CAUTION #3: It is also quite common from what I have seen among alternative practitioners to adminster low dose hydrocortisone for a month or two and then stop. The reason for this is that often men experience a "restart," where their adrenal function normalizes and they then begin to produce normal levels of cortisol again.
CONCLUSION: Many men suffer from crushing fatigue and mental fog. This often results from low cortisol and low dose hydrocortisone therapy can literally bring these men back to life. Dr. Jeffries argues that this kind of therapy, when done properly, is very safe. There seem to be analogies with standard TRT (testosterone replacement therapy). However, one can make the case that low dose hydrocortisone should only be give for a few months and pregnenolone can sometimes be given as an adjunct therapy.