I think the trick here is that the resistors are much more precise than two batteries of unknown origin will be at providing a symmetric supply voltage without further stabilization. So they serve as a 50/50 voltage divider
whatever the input voltage is, 7+9 or 6+8 on half full (or half empty, depending on your mental make-up) batteries, it would still work just fine.
Binding the central line between the two 9V batteries to GND would give you the situation you describe, indeed you could then drop the resistors but now you have a fairly high risk of ending up with an asymmetric supply voltage, which means one side will clip earlier than the other.