I think this is a major misconception. Clen is commonly used post cycle when you are in a catabolic state, however this does not mean that it in any way reduces cortisol levels.
Clenbuterol is a beta agonist, with specific affect and affinity to Beta 3 receptors. These beta-3 receptors increases insulin secretion and sensitivity, causing more glucose and amino acids to be transported into skeletal muscle thus causing the anabolic effects. (Note that Clen's fat burning properties are linked to beta 2 receptor activity.)
Clen is widely used in the cattle industry becuase it leans out the cattle (beta 2) while increasing muscle mass (beta 3). There is a dramatic affect on cattle becuase they have a LOT of beta 3 receptors. Unfortunately, humans have a lot fewer beta 3 receptors, we have mainly beta 2, which do not react as strongly to clen. However, when your Beta 2's are saturated there is some thought that this can cause an upregulation of the Beta 3's. This is why it is significantly anabolic to cattle, and mildly anabolic at best in humans.