In some cases it can be true. At least, in my experience that was the problem. I developed a stutter in late puberty due to some bad things that happened at that time and let to chronic depression and low self esteem. However, the last 5-6 years (now I'm 38) things got much better in my life and the stuttering has almost disappeared. It occurs occasionally only when I'm in environment where I don't feel comfortable, but that happens less and less.