The reasons
The max rate/ min radius is to be considered in level fligth only.
Rate of turm is indirectly proportional to airspeed, and directly proportional to angle of bank. That is simply put, the higher you airspeed the lower is you rate of turn, and the higher your angle of bank, the higher your rate of turn.
Radius of turn is directly proportional to airspeed and indirectly proportional to angle of bank. Put simply once again, the higher your airpseed, the larger is your radius of turn and the higher your angle of bank, the lower your radius of turn.
In order to achieve your lowest airspeed, in level flight, you must be configured with gear up, and full flap. You must then roll into the turn and apply full power,(to lower your stall speed further). Remember he stall anlge is the same for your configuration. When you are immediately at the critical angle, and holding it, in level flight, you will then be at max rate and min radius.
It is all very elementary, but can be made as complex as you want, the basic facts however, are always right!!
best wishes.