Complete gobbledegook in fact.
What does "drop the voltage without the regulator" mean? The regulator is basically useless and should be removed to get rid of its minor current draw, but how the ATmega responds to its supply voltage has absolutely nothing to do with whether that voltage is controlled by that regulator or something - anything - else.
And the Arduino does not switch its clock frequency in any manner relative to its supply voltage.
There is a certain minimum voltage at which it will function with a 16 MHz clock, it will simply not work at a certain lower voltage. You can use a different crystal - such as an 8 MHz - if you want it to operate at lower voltages, but you have to provide that clock or code it to use the internal approximately 8 MHz timebase.