I thought of a simpler way of saying it:
With a 100% efficient charging system you get as much out of the batteries as you put in.
No charging system is 100% efficient , so you get slightly less out of the batteries then you put in.
Lets say charging efficiency is at 90%
1 unit of fuel = 1 unit of energy
If you burn 100units of fuel you will put 90units of energy in the battery.
If you can go 1 mile one one unit of fuel/energy you will go 90 miles, but burn 100 units of fuel.
10 units of fuel have been lost as heat because the charging system is only 90% efficient.
On the surface you will go 100 miles on 100 units of fuel because you don't have the 10% loss in charging the batteries.
Claiming you go further running on batteries is saying that you get more out of your batteries than you put in. This is obviously impossible!
*edit* sorry, my spell check bugger things up for a second there