Is there a shell between the kernel and hardware
Given the details you have given us, you are of course right.  There is no shell between the hardware and the kernel; that's just silly.  Asking "but what if there were?" would be like asking "but what if pigs could fly?".

It is likely that either there was some misunderstanding or that the examiner is confused.  The former is much, much more likely.

One thing I might critique is your characterization of a shell as an interpreter.  While a shell is an interpreter, not every interpreter is a shell.  I suppose it is possible that the examiner was asking a follow-up question to see if you understand that.

As far as how a kernel runs programs.... read a standard operating system textbook.  The details are adequately covered in any standard OS textbook.

The thing is... I'm not sure why you're asking us. Why not ask your professor or examiner?  We can't tell you what was in your examiner's head.