The output thermal current noise increases with the current, but the transistor transconductance also. Then, you calculate the input noise dividing by gm^2, thus the input noise decrases.
Consider the MOS thermal noise: SIDout = 8/3 kT gm = 8/3 kT 2ID/(VGS-VTH) and SVin = SIDout/gm^2 = 8/3 kT / gm = 8/3 kT * (Vgs-VTH)/2ID. This is valid in strong inversion and saturation.
The same holds for the bjt with slightly different formulas and for MOS in weak inversion.