The air carrier access act just says "thou shalt not discriminate against disabled passengers." The details (if anybody is intereted) are down in the FAA regulations 14 CFR 392.117. The FAA is pretty clear on the recency of the letter, who prepares it, and what it contains.
(e) If a passenger seeks to travel with an animal that is used as an emotional support or psychiatric service animal, you are not required to accept the animal for transportation in the cabin unless the passenger provides you current documentation (i.e., no older than one year from the date of the passenger's scheduled initial flight) on the letterhead of a licensed mental health professional (e.g., psychiatrist, psychologist, licensed clinical social worker, including a medical doctor specifically treating the passenger's mental or emotional disability) stating the following:
(1) The passenger has a mental or emotional disability recognized in the Diagnostic and Statistical Manual of Mental Disorders - Fourth Edition (DSM IV);
(2) The passenger needs the emotional support or psychiatric service animal as an accommodation for air travel and/or for activity at the passenger's destination;
(3) The individual providing the assessment is a licensed mental health professional, and the passenger is under his or her professional care; and
(4) The date and type of the mental health professional's license and the state or other jurisdiction in which it was issued.
Note that "I get stressed" is not a DSM disorder. Stress is a part of life. The stress and anxiety disorders in the DSM are pretty detailed in that you have to have severe issues functioning as a result of them before the diagnosis can properly be made.

