Do I need 3/4 inch plywood subfloor?
If you are interested in the science behind your question, the answer lies hidden in your question.  You mentioned "is the extra 1/4 inch really needed".  

As do most people, you translated this in your mind to "I know how little stiffness there is in a wimpy piece of 1/4 inch plywood, so how could it really make any difference".

The stiffness of a piece of material is only determined by simple addition in a case where the two layers are free to slide against each other.  If just laid one on top of the other with no connection between them, two 1/4 inch thick pieces of plywood form a combination that is merely twice as stiff.

In the more common case of well attached or glued layers (or in this case just a thicker single sheet of plywood), doubling the thickness of a sheet MUCH more than doubles its stiffness.  The 3/4 plywood is more than twice as stiff as 1/2" plywood.