Alex, the device does in fact have a regulator, the core runs at 1.2 volts, this is what mostly accounts for very similar current across Vdd range.
You are probably not using a lot of MCU pins in your tests. Switching outputs at different Vdd values would show a more linear current drop.
I should also point out that the current is in fact dropping a little bit, with the voltage dropping, the overall power is lower.