Very relevant and recurring topis for discussion. Having seen the replies fully, I can understand the forum is absolutely divided in their opinion.
I believe HR is a function representing Human Resources to the Management but often it is misunderstood and considered as other way around (representing Management). Compassion & empathy should be the way someone can win hearts but not by policing, authority & commanding. In this case, the alter-ego of HR Manager is visible clearly. It is very common for an employee to behave immaturely but I am surprised learning the HR Manager too was at his immature best. He neither showed compassion nor followed standard process.
Firstly either he can approve or disapprove the employee resignation 1st instance itself. If he disapproves, then there is a chance he can Terminate the employee. However, to go to that level, firstly a domestic inquiry along with proper hearing (with a facility for employee to call for 2nd inquiry) should happen. To complete the entire process, 45 days will anyway happen for the HR to Terminate the employee. Finally, HR Manager wins the long haul battle just to satisfy his ego by wasting so much office resources (time, material & money).
An issue which can be closed with just couple of phone calls or 1 to 2 direct discussions have transformed to this level. Whom to blame here?