VTEC and VVT-i are only a part of the whole system. They mainly control actuation of the intake/and or exhaust valves (duration, lift). The ECU will determine how much fuel to add with input from the MAF or MAP sensor and intake air temperature. The variable valve timing doesn't add any fuel at all - it just controls the duration - basically how long during the cycle it stays open (duration) and far to project into the cylinder (lift) - on some models.
Actually most modern EFI system are very efficient - they constantly optimize the air/fuel mix for a given situation. But that can only give you so much - variable valve timing technology will allow you to extract more power and efficiency from the motor. By having variable valve operation - you can optimize the vehicle for low RPM and high RPM operation - places where just varing the fuel cannot achieve.
The moniker "variable fuel" could be just a model that can run on either gas or ethanol or some other fuel. Before the hybrids came out - engineers where experimenting with alternative fuels. Cars that could run on CNG, propane, ethanol, jet fuel, etc. Just do a search for "alternate-fuel vehicles".
Good Luck.