Arduino pro mini v5 on-board MIC5205 150mA LDO Regulator

But the battery datasheet says "Never discharge Li‐Po battery below the Lowest Discharge Voltage 3v per cell"

and the voltage regulator data says "takes an input voltage from 2.7 V to 11.8 V and increases or decreases the voltage to a fixed 5 V output'

Thus wouldn't the Voltage regulator discharge the battery to 2.7V causing irreversible damage which will deteriorate the battery performance and cycle life ?

http://www.overlander.co.uk/fullymax_warning_sheet_li_poly.pdf