People with breathing difficulties are often told to take a deep breath. Is this wrong?

From the perspective of the Buteyko Method, it is wrong. While the concept of deep breathing, or just taking a deep breath, has become a part of our popular culture, excessive breathing could be harmful to people with breathing difficulties and others. K. P. Buteyko MD-PhD pointed out (based on the Bohr Effect)  that oxygenation of the vital organs decreases when breathing increases. In fact, deep breathing can easily provoke various breathing problems and worsen other health conditions.