Not true, it will only give 0 when the 0 end of the pot is pressed.
As @kmin suggested they require a resistor between the wiper (center pin) and ground to read 0 when not pressed. However, that will now make the response non-linear, not good if you are trying to simulate a violin
int value1 = analogRead(A0);
int value1 = analogRead(A0);
int value2 = analogRead(A1);
int value2 = analogRead(A1);
The ADC multiplexer needs time to read and acquire the analog input value selected.
By reading the the input twice, this gives the ADC the time to acquire the newer value.