AllenF — What you're saying cannot be true. Ultimately, in a round trip, all the energy used by the vehicle comes from the gasoline, including all the energy recovered by regenerative braking. The battery is also sometimes recharged directly by the ICE. But since the mechanical-to-electrical (and electrical-to-mechanical) conversion processes in the motor-generators aren't 100% efficient, and the battery charge/discharge process loses energy to heat too, you are only going to be better off FE-wise by using EV-mode as much as possible if you can arrange things so that battery recharging occurs when the ICE is running at greater efficiency than it would otherwise have been achieving had you not used EV-mode. This can apparently be done in the FEH more easily than in some of the other hybrids out there, whose ECUs optimize overall FE somewhat better. However, your assumption that you are increasing FE simply by using EV-mode more, is false.

Stan