Not actually true.
That part of Cd representing lift dependent drag increases with the square of Cl. If you're in level flight and slow down, then up must go AoA and hence Cl if you wish to maintain level flight.
Cdi = k Cl**2/pi * AR (k is a constant, Cl**2 means Cl squared, pi means 3.14159 and AR is the aeroplane's aspect ratio.)
Which is why there's a 'min drag speed' for any aeroplane.