Which comes first?
Gemba Panta Rei has an article that is relevant to, People or Process, a recent post on this blog. I think this highlights the benefit of looking at process or environment first when you have a people issue.
"in Japan the first response to a high rate of absenteeism is to conduct root cause analysis into the behavior of absenteeism, leading to kaizen. In Europe the management would replace the worker who had an attendance problem with another workers. Problem not solved, but deferred."
If its a flawed process, or if you have a flawed understanding of competencies necessary to perform the job, switching people out does not solve the problem. Combining a quality process with a clear understanding of the innate competencies and values required to be successful in the job is a powerful combination. Much more powerful than either applied independently.