How are people working in psychophysics trained? It is unclear to me how people in psychophysics are trained. Are they psychologists, or physicists, or physicians, or biologists, or physiologists? Or can they be any of those?

What if someone doing psychophysics (according to his own accord) is making statements about biological pathology?

Is Psychophysics currently a credible scientific field?
Short answer
Psychophysics is a multidisciplinary field featuring people with a Physics, Psychology, Medicine and/or Biology background. 

Background
OK, here follows a lot of personal account to illustrate where psychophysicists may come from.

Traditionally, psychophysics is a part of Psychology. 

I do a lot of psychophysics and I'm a Biologist by training (MSc), but learned psychophysics during a postdoc. My supervisor teaching me psychophysics was a physicist (MSc) who acquired their skills during their PhD (in visual sciences).   

My current supervisor is a physicist by training (MSc), but has done heaps of psychophysics as part of his post-grad Audiology training.

Many of my psychophysics colleagues are in fact physicists.