First of all, I have a degree in Industrial Engineering. While that isn't my line of work, I am quite certain that having a degree in Industrial Engineering does not make it illegal or inappropriate for a person to conduct investigations, so his educational background isn't really relevant. In the years between 1971 and 2002 I'm sure he could have learned a great deal to supplement his degree.
I'm sure that in time his specific job description, and the normal scope of his duties for the University will come out, and then we will have more to go on. Even then, though, the discussion here really isn't whether or not Schultz had the actual authority to conduct an investigation, but whether Paterno had reason to believe that he did. That is also a question that I can't answer.
Leaping lizards, you are having trouble getting this one!
What makes it illegal and inappropriate for him to do police work is that he's not a police officer. I included that tidbit about his background because I'm trying to explain to you that he's not a police officer.
Here's more, directly from Penn State's Web site:
"Gary C. Schultz, who retired from Penn State in 2009 after nearly 40 years of service, has been named interim senior vice president for Finance and Business while the University conducts a national search to fill the position ... Schultz served as senior vice president for finance and business from 1995 until his retirement and led the division that includes the offices of Human Resources, Physical Plant, University Police, Investment Management, Auxiliary and Business Services, Corporate Controller, University Budget, Legal Services and Commonwealth Campus Business Operations ... Schultz, who earned a bachelor's and master’s degree in industrial engineering from Penn State, began his career with the University in 1971 and through 1995 handled various administrative responsibilities related to business operations, finance and technology, before being named to the vice president role in 1995."
Schultz conducting a criminal investigation would be like a city council member, deputy mayor or member of a police commission conducting a criminal investigation in lieu of the municipal police.
Just knowing his job title - let alone the job description given in his bio - is enough to infer that he is not a cop in any way, shape or form.