No, they are not immune to depression, but there is a fairly clear link between mental illness and socioeconomic status. People who come from a background of poverty have a significantly higher risk - this is the case in most areas.
This group also has significant purchasing power to pay off waiting lists, and obtain the best possible and available treatment. Now I am aware that being a top athlete means a lot of pressure, and many are struggling. However, they are usually privileged. Because they usually have the opportunity to use the best therapists, do not have to wait, and they usually have a whole apparatus that takes care of their interests.
So what I wrote was obviously a bit of nonsense, but there was also some truth in it. There is a lot of [Poor language removed] in the world, but privileged football players are not the first ones I plan to march for.