Does my refrigerator's water line require a shutoff valve behind the refrigerator?
Yes.  Sort of.  It doesn't require it to be behind the fridge, but it does require one on the supply.

Uniform Plumbing Code
606.0 Valves
606.5 Control Valves. A control valve shall be installed ahead of each water-supplied appliance and immediately ahead of each slip joint or appliance supply.

Unless your county has amended the code.