The author identified the problem pretty directly:
We have a couple of problems. The first is that our employee termination process is broken. Ideally, we would have an identity management tool tied into our various enterprise systems. When an employee left the company, all access to our infrastructure and applications would be quickly removed. Unfortunately, we have neither the budgetary nor the human resources to do that.
I'd say that's a problem! I wonder if they have budget now?